Inclusion Criteria:  Willing to sign the ICF and follow the requirements specified in the protocol. Age: ≥18 years, both genders. Expected survival time>3 months. Patients with histologically confirmed unresectable, radiation-ineligible recurrent metastatic nasopharyngeal carcinoma. Part A: Metastatic nasopharyngeal carcinoma that has failed or recurred or was intolerant to at least two lines of prior systemic therapy with platinum-based regimens. Part B: Cohort 1: Metastatic nasopharyngeal carcinoma that has failed or recurred or was intolerant to prior systemic therapy with a first-line platinum-based regimen. Cohort 2: Metastatic nasopharyngeal carcinoma that has failed or relapsed after or is intolerant to at least two prior lines of platinum-based systemic therapy. Patients must have measurable lesions according to the Response Evaluation Criteria in Solid Tumors (RECIST v1.1). ECOG performance score 0 or 1. Organ functions and coagulation function must meet the basic requirements. No severe cardiac dysfunction with left ventricular ejection fraction (LVEF) ≥ 50%. Serum or urine pregnancy test negative within 72 hours before the first dose of investigational drug. Patients with childbearing potential must use effective contraception during the treatment and for 6 months after the last dose of treatment.  Exclusion Criteria:  Part A: received < 2 prior lines of systemic therapy. Part B: Cohort 1 received two lines of prior therapies; Cohort 2 received the first line of prior therapy only. History of 4 or more systemic anti-tumor therapies for the recurrent metastatic nasopharyngeal carcinoma. Expected surgery or any other form of systemic or local anti-tumor therapy. History of systemic chemotherapy, antitumor biological therapy or immunotherapy, or major surgery within 3 weeks, >30 Gy thoracic radiotherapy within 6 months, prior radiotherapy within 14 days before the first administration of the investigational drug. Known active CNS metastasis and/or cancerous meningitis. Residual toxicity reactions caused by previous anti-tumor treatment or abnormal values of laboratory tests higher than grade 1 (CTCAE v5.0). Uncontrolled or poorly controlled heart disease. History of pulmonary embolism or deep vein thrombosis within 3 months before the first administration of the investigational drug. Known history of malignancy. Uncontrolled or poorly controlled hypertension. Patients with a history of active bleeding, coagulopathy, or receiving coumarin anticoagulation therapy. Subjects with a history of ≥ Grade 3 immune-related AEs (irAEs). Known allergic reaction to any ingredients or excipients of MRG003. Known active hepatitis B or C. Complicated with severe, uncontrolled infection or known human immunodeficiency virus (HIV) infection, or diagnosed as acquired immunodeficiency syndrome (AIDS); or uncontrolled autoimmune disease; or history of allogeneic tissue/organ transplantation, stem cell or bone marrow transplantation, or solid organ transplantation. Active bacterial, viral, fungal, rickettsia, or parasitic infections that require systemic anti-infective treatment. Vaccination of live virus vaccine within 30 days before the first administration of the study drug. Inactivated seasonal influenza vaccine or approved COVID-19 vaccine is allowed. Moderate to severe dyspnea at rest caused by advanced cancer or its complications, or severe primary lung disease, oxygen saturation < 93% in non-oxygen state, or history of any interstitial lung disease or interstitial lung disease (ILD) requiring oral or intravenous glucocorticoids or non-infectious pneumonia. Patients receiving immunology-based treatment for any reason. Chronic autoimmune disease or inflammatory disease requiring systemic therapy or receiving systemic therapy within the past 2 years. Uncontrolled pleural effusion, pericardial effusion or recurrent ascites. Potent CYP3A4 inhibitors or inducers are in use and cannot be discontinued. Women who are lactating or pregnant. Other conditions that in the clinical judgement of the investigator make the patient not suitable for participation in this study.