Inclusion Criteria:  Understands and provides written informed consent and willing to follow the requirements specified in protocol; Both genders; Aged 18 to 75 (including 18 and 75); Expected survival time ≥ 12 weeks; Patients with histologically and/or cytologically confirmed HER2-positive solid tumors who have failed standard therapy or for whom no standard therapy exists or for whom standard therapy is not appropriate at current stage; Patients must have at least one evaluable lesion (Phase Ia) or measurable lesion (Phase Ib) according to the Response Evaluation Criteria in Solid Tumors (RECIST 1.1); The score of ECOG for performance status is 0 or 1; Prior anti-tumor treatment-related AEs (NCI CTCAE v5.0 Criteria) have recovered to ≤ Grade 1 (except alopecia); No severe cardiac dysfunction with left ventricular ejection fraction (LVEF) ≥ 50%; Organ functions must meet the basic requirements; Coagulation function must meet the basic requirements; Cumulative anthracycline dose ≤ 360 mg/m2 doxorubicin or its equivalent, 720 mg/m2 epirubicin.  Exclusion Criteria:  Received radiotherapy, chemotherapy, biotherapy, immunotherapy, or other anti-tumor drugs within 3 weeks prior to the first dose of MRG002 treatment; History of severe cardiac disease; Clinically significant abnormalities in rhythm, conduction, and resting ECG morphology; Patients with poorly controlled hypertension or clinically significant vascular disease; History of moderate to severe dyspnea at rest due to advanced cancer or their complications, severe primary lung disease, or current need of continuous oxygen therapy, or any history of interstitial lung disease (ILD) or pneumonitis; Nausea and vomiting of any kind difficult to control, or chronic gastrointestinal disease; Patients with symptoms of central nervous system or brain metastasis or received treatment for central nervous system or brain metastasis within 3 months prior to the first dose of MRG002 treatment; Major surgery not fully recovery within 4 months prior to the first dose of MRG002 treatment; History of hypersensitivity to any component of MRG002 or history of hypersensitivity of ≥ Grade 3 to trastuzumab injection; Evidence of active infection of hepatitis B or hepatitis C; History of immunodeficiency, including human immunodeficiency virus (HIV) infection, or other immunodeficiency disease, or history of organ transplantation; Any serious and/or uncontrolled disease or other condition that, considered by the investigator and sponsor, may compromise the patient's participation in this study; Received systemic corticosteroids within 4 weeks prior to the first dose of MRG002 treatment; Female patients with a positive serum pregnancy test or who are breast-feeding or who do not agree to take adequate contraceptive measures during the treatment and for 6 months after the last dose of study treatment. Other conditions inappropriate for participation in this clinical trial, at the discretion of the investigator.