Inclusion Criteria:  Males or females aged ≥ 18 years at the time of signing the informed consent form. For Part 1 of this study, the subjects should be ≤ 75 years of age. Patients for Part 1: patients histopathologically diagnosed with advanced or recurrent solid tumors. For Part 2 of the study, Patients with non- functional metastatic neuroendocrine tumor confirmed by histopathology. Patients must be able to provide archived tumor tissues after latest treatment or fresh tumor tissues and relevant pathology report. Patients whose estimated survival time is more than 3 months. Patients with at least one measurable lesion at baseline according to RECIST (Version 1.1). The lesion had not previously received surgery, radiotherapy and/or local treatment. Patients with Eastern Cooperative Oncology Group(ECOG) performance status score ≤1. Every woman or man with potential fertility needs to use an effective contraceptive method during the study, up to within 3 months after last drug administration. Willing and able to comply with study-specified visits schedule, treatment plan, laboratory examination and other study procedures.  Exclusion Criteria:  Patients who are simultaneously participating in another clinical study. Patients with a history of severe allergic diseases, a history of severe drug allergies, and known or suspected allergy to macromolecular protein preparations or HBM4003 or Toripalimab or its excipients.  Previous and concomitant drugs or treatments to be excluded like:  Anti-CTLA4 drug; For part 1, anti-PD1 anti-PDL1 or anti-PDL2 treatment was received within 8 weeks prior to the start of the study; For part 2, patients received anti-PD1, anti-PDL1 or anti-PDL2 treatment during the relapse or metastasis stage, and the time from the last treatment is short than 12 months before the first dose; Received other antitumor treatment (including chemotherapy, radiation, targeted therapy, or biotherapy), antitumor vaccine, chinese herbal medicine or proprietary medicine with anti-tumor effect, Immunosuppressant or glucocorticoid, Transfusion of PLT or RBC prior to initiation of study treatment; live attenuated vaccine was received before study administration or planned during the study period. Insufficient recovery from previous treatments. Diseases that may affect the efficacy and safety of the investigational product, including but not limited to active infection, active autoimmune disease or autoimmune disease, primary immunodeficiency disease, any clinically significant cardiovascular disease, severe pulmonary insufficiency, organ transplantation, etc. A history of other malignant diseases within 5 years before the first dose. Symptomatic, active, or urgent treatment-requiring central nervous system (CNS) metastasis with imaging evidence (based on CT or MRI assessment). Subjects with pleural effusion, pericardial effusion, or ascites that could not be stabilized by repeated drainage or other methods were determined by investigator. Patients who the investigator believes may have other factors that will affect the efficacy or safety evaluation of this study (e.g., mental disorders, alcoholism, drug use, etc.). Women who are pregnant or breastfeeding, or who plan to become pregnant during the study period and within 3 months after the last administration of the investigational product.