• Phase 1, Safety and tolerability: dose limiting toxicity [ Time Frame: 28days post administration of CAR-T-cells ]
  dose limiting toxicity
• Phase 2, efficacy of CT053 CAR-BCMA T cells: overall response rate [ Time Frame: 3 months post administration of CAR-T-cells ]
  overall response rate (ORR)=（sCR+CR+VGPR+PR)

• Phase 1, Safety and tolerability: dose limiting toxicity [ Time Frame: 28days post administration of CAR-T-cells ]
  dose limiting toxicity
• Phase 2, efficacy of CT053 CAR-BCMA T cells: overall response rate [ Time Frame: 12 months post administration of CAR-T-cells ]
  overall response rate (ORR)=（sCR+CR+VGPR+PR)

• Additional efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion [ Time Frame: 3 months post administration of CAR-T-cells ]
  Minimal residual disease (MRD) negativity
• Additional efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion [ Time Frame: 3 months post administration of CAR-T-cells ]
  TTR TIme to Response
• Additional efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion [ Time Frame: 3 months post administration of CAR-T-cells ]
  Complete Response (CR) /stringent Complete Response (sCR)
• Additional efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion [ Time Frame: 3 months post administration of CAR-T-cells ]
  ≥Very Good Partial Response (VGPR), including VGPR, CR, sCR
• Additional efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion [ Time Frame: 3 months post administration of CAR-T-cells ]
  ORR at Wk12
• Additional efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion [ Time Frame: 3 months post administration of CAR-T-cells ]
  CBR, clinical benefit rate
• Safety and tolerability of CAR-BCMA T cell therapy [ Time Frame: through 24 months post administration of CAR-T-cells ]
  AE&SAE
• Pharmacokinetics (the cell persistence duration in peripheral blood) [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Copy numbers of CAR-BCMA gene in peripheral blood
• Pharmacokinetics (the cell persistence duration in peripheral blood) [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Number of CAR positive cells in peripheral blood
• Safety and tolerability of CAR-BCMA T cell therapy [ Time Frame: through 24 months post administration of CAR-T-cells ]
  positivity of ADA (Anti-CAR-T antibody)
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Overal response rate (ORR)
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Complete Response (CR) /stringent Complete Response (sCR)
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  ≥Very Good Partial Response (VGPR), including VGPR, CR, sCR
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Duration of Response (DOR)
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Clinical Benefit Rate (CBR)
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Time to Response (TTR)
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Minimal residual disease (MRD) negativity
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Progression Free Survival (PFS)
• Efficacy endpoint of CAR-BCMA T cells after infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Overall Survival (OS)

• Efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion: Overall Response Rate [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Overall Response Rate(ORR), ORR=(sCR+CR+VGPR+PR)/total subjects.
• Efficacy evaluation after 12 weeks of CT053 CAR-BCMA T cells infusion: Response rate [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Response rate of VGPR, CR and sCR.
• Pharmacokinetics (the cell persistence duration in peripheral blood) [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Duration of CAR-BCMA T-Cell persistence is the period from the day of infusion to the first negative test result or result lower than the detection limit.
• Pharmacokinetics (the number of cell copies in peripheral blood) [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Pharmacokinetics is the "Implantation endpoint" which is defined as the number of copies of CAR-BCMA DNA in peripheral blood detected by q-PCR and flow cytometer at each visit after infusion until any two consecutive test results are negative or below the detection limit.
• Safety and tolerability after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Occurrence rate and severity of AE [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Occurrence rate and severity of AE after infusion.
• Safety and tolerability after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Occurrence rate and severity [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Occurrence rate and severity of treatment related AE.
• Safety and tolerability after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Treatment related SAE. [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Treatment related SAE.
• Safety and tolerability after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Occurrence rate and severity [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Occurrence rate and severity of AEs of special interest (CRS, CRES, etc.)
• Safety and tolerability after 12 months and 24 months of CT053 CAR-BCMA T cells infusion [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Abnormal results of laboratory test.
• Safety and tolerability after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Positive rate [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Positive rate of Anti-CT053 CAR-BCMA T cell.
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Overall Response Rate [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Overall Response Rate(ORR), ORR=(sCR+CR+VGPR+PR)/total subjects.
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Duration of Response [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Duration of Response (DOR)
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Clinical Benefit Rate [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Clinical Benefit Rate (CBR), CBR=ORR+MR
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Time to Response [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Time to Response (TTR)
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: MRD negative rate [ Time Frame: through 24 months post administration of CAR-T-cells ]
  MRD negative rate
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Progression Free Survival [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Progression Free Survival (PFS)
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Overall Survival [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Overall Survival (OS)
• Efficacy evaluation after 12 months and 24 months of CT053 CAR-BCMA T cells infusion: Response rate [ Time Frame: through 24 months post administration of CAR-T-cells ]
  Response rate of VGPR, CR and sCR.

Inclusion Criteria:

1. Patients and legally acceptable representative must have voluntarily signed ICF and willing to complete the study procedure, after fully understanding of the study.
2. Age ≥ 18 years and ≤ 75 years, male or female
3. The patients have received at least 3 prior regimen for MM, (Induction therapy followed by autologous transplantation[ASCT] and maintenance therapy represents one line of therapy, those who have not been treated with ASCT should have documented rationale); For each line of therapy, the patient should have received at least one standard treatment cycle (2016 IMWG) unless the best response to the treatment line is documented as progressive diseases (PD)
4. The patients should have received treatment with at least one proteasome inhibitor AND one immunomodulatory drug, and have ever been relapsed or deteriorated after treatment with at least one regimen consisting of above-mentioned medications (combination or single use)；
5. Patient should be relapsed within 12 months after the last line of therapy, or not achieved at least minimal response (MR) or disease progressed within 60 days after last line of therapy (IMWG criteria 2016), with documented evidence.

6. The patients should have measurable disease based on at least one of the following parameters：

   • Serum M-protein ≥ 10 g/L;
   • Urine M-protein ≥ 200 mg/24 hrs;
   • For those whose Serum or Urine M- protein dose not meed the measurable criteria but the light chain type, serum free light chain (FLC): involved FLC level ≥ 10 mg/dL (100 mg/L) provided serum FLC ratio is abnormal
7. Estimated life expectancy > 12 weeks
8. ECOG performance score 0-1；
9. Sufficient venous access for leukapheresis collection, and no other contraindications to leukapheresis
10. Patients should maintain adequate organ function
11. Women of childbearing age must undergo a serum pregnancy test with negative results before screening and lymphodepletion preconditioning with fludarabine and cyclophosphamide, and are willing to use effective and reliable method of contraception for at least 1 year after T cell infusion
12. Men who actively have intercourse with child-bearing potential women must be willing to use effective and reliable method of contraception for at least 1 year after T cell infusion

Exclusion Criteria:

1. Pregnant or lactating women；
2. P2. Positive for any following tests: human immunodeficiency virus (HIV) antibody, Treponema Pallidum antibody, hepatitis C virus (HCV) antibody, hepatitis B virus (HBV) surface antigen (HBsAg), HBV e antigen (HBeAg), HBV e antibody, hepatitis B core antibody, HBV DNA;
3. Patients with any uncontrolled active infection including but not limited to active tuberculosis.
4. Patients with AEs from previous treatment that have not recovered to Common Terminology Criteria for Adverse Events (CTCAE) ≤ 1, excluding hair loss, neuropathy and other events that the treating physician can determine to be tolerable.
5. Patients who have ever had any CAR T cell therapy；
6. Patients who have ever had anti-BCMA therapy；
7. Patients have received allogeneic stem cell transplantation for treating multiple myeloma;
8. Patients have received autologous stem cell transplantation less than 12 weeks before leukapheresis；
9. Patients have received any anti-cancer treatment within 14 days before leukapheresis including but not limited to cytotoxic therapy, proteasome inhibitors, immunomodulatory agents, targeted therapies, epigenetic therapy or experimental drug therapy. If the field of radiation covers ≤ 5% of the bone marrow, the subjects are eligible to participate in the study regardless of the radiotherapy end date；
10. Patients have received ≥ 5 mg prednisone daily or other equivalent dose of steroids within 14 days before leukapheresis or lymphodepletion；
11. Patients have plasma cell leukemia, Waldenström macroglobulinemia, POEMS (polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes) syndrome or AL amyloidosis；
12. Patients have been administered live attenuated vaccine 4 weeks before leukapheresis or lymphodepletion
13. Patients allergic to component of study treatment.
14. Patients have any of the condition as following within 6 months of ICF sign-off: New York Heart Association (NYHA) stage III or IV congestive heart failure, angina pectoris, myocardial infarction, coronary artery bypass graft, stroke (excluding lacunar stroke), history of clinically significant arrhythmia including but not limited to ventricular arrhythmia, significant QT interval prolongation, uncontrolled blood pressure as defined as systolic > 160 mmHg, diastolic > 100 mmHg, uncontrolled diabetes mellitus, pulmonary thrombolism, other conditions that investigators believe that participating in this clinical trial may endanger the health of the patients
15. Patients are known to have active autoimmune diseases including but not limited to psoriasis, rheumatoid arthritis and other needs of long-term immunosuppressive therapy
16. patients are oxygen dependent as defined by the blood oxygen saturation (finger oxygen detection method) can be maintained > 95% only by oxygen inhalation before leukapheresis
17. Patients with second malignancies in addition to MM are not eligible if the second malignancy has required treatment within the past 5 years or is not in complete remission. There are two exceptions to this criterion: successfully treated cervical carcinoma in situ and non-metastatic basal cell skin carcinoma
18. Patients have central nervous system (CNS) metastases or CNS involvement (including cranial neuropathies or mass lesions and leptomeningeal disease). Patients with history of spinal cord compression from MM are eligible provided spinal cord compression has been treated with surgery or radiation at least 28 days prior to study entry
19. Patients are unable or unwilling to comply with the requirements of clinical trial
20. Patients have received major surgery 2 weeks prior to leukapheresis or 4 weeks prior to lymphodepletion and after the study treatment (excluding cataract and other local anesthesia)
21. Patients are relatives to investigator or his/her staff, or those who may have an interest in the investigator and/or his/her staff.

• Beijing Chao Yang Hospital
• The First Affiliated Hospital of Soochow University
• Xinhua Hospital, Shanghai Jiao Tong University School of Medicine
• Tianjin Medical University General Hospital
• First Affiliated Hospital of Zhejiang University
• Beijing Hospital
• Shanghai Tongji Hospital, Tongji University School of Medicine
• First Affiliated Hospital of Wenzhou Medical University
• Xiangya Hospital of Central South University
• Peking University People's Hospital
• Qilu Hospital of Shandong University
• Sun Yat-sen University
• First Affiliated Hospital, Sun Yat-Sen University