Inclusion Criteria:
1. Age ≥18 years;
2. Histologically or cytologically confirmed adenocarcinoma of prostate；
3. Documented progressive metastatic CRPC based on Prostate Cancer Working Group 3(PCWG3) criteria, which includes at least one of the following criteria: a.PSA progression;b.Objective radiographic progression in soft tissue; c.New bone lesions
4. Have serum testosterone \< 50 ng/dL;
5. Patients with significant PSMA avidity on 68Ga-NYM032 PET/CT；
6. ECOG score of 0 or 1；
7. Expected life≥ 6 months;
8. Patients must have received at least one NAAD；
9. Patients must have received taxane-based chemotherapy or not be candidates for taxane chemotherapy；
10. Patients must have adequate organ and marrow function；
11. The subjects agree to take effective contraceptive measures during the study period and for at least three months after the drug administration:
12. The subjects are able to maintain good communication with the researchers, understand and follow the requirements of this study, voluntarily participate, and sign an informed consent form before the start of relevant research operations.
Exclusion Criteria:
1. Previous treatment with any of the following within 6 months before enrollment: Strontium-89,Samarium-153,Rhenium-186,Rhenium-188, Radium-223,hemi-body irradiation. Previous PSMA-targeted radioligand therapy is not allowed;
2. Any systemic anti-cancer therapy(e.g.chemotherapy, immunotherapy or biological therapy \[including monoclonal antibodies\]) within 28 days prior to day of enrollment;
3. Site(s) of disease that are FDG positive with minimal PSMA expression ;
4. Any investigational agents within 28 days prior to day of enrollment;
5. Known hypersensitivity to the components of the 177Lu-NYM032 or its analogs;
6. Other concurrent investigational therapy;
7. Transfusion for the sole purpose of making a subject eligible for study inclusion;
8. Patients with a history of Central Nervous System (CNS) metastases must have received therapy (surgery, radiotherapy, gamma knife) and be neurologically stable,asymptomatic, and not receiving corticosteroids for the purposes of maintaining neurologic integrity, Patients with epidural disease, canal disease and prior cord involvement are eligible if those areas have been treated, are stable, and not neurologically impaired. For patients with parenchymal CNS metastasis (or a history of CNS metastasis), baseline and subsequent radiological imaging must include evaluation of the brain (MRI preferred or CT with contrast);
9. A superscan as seen in the baseline bone scan;
10. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression;
11. Concurrent serious (as determined by the Principal Investigator) medical conditions that in the opinion of the investigator would impair study participation or cooperation;
12. Diagnosed with other malignancies that are expected to alter life expectancy or may interfere with disease assessment. However, patients with a prior history of malignancy that has been adequately treated and who have been disease free for more than 3 years are eligible, as are patients with adequately treated non-melanoma skin cancer, superficial bladder cancer;
13. Eligible for treatment(s) other than ARDT based on the presence of any mutations or biomarkers that are known as predictors of better response (e.g., AR-V7 or BRCA).
