A Study to Evaluate Safety, Tolerability, PK/PD and Preliminary Efficacy of HBM4003 Combined With Anti-PD-1 Antibody

Inclusion Criteria: * Male or female patients ≥18 years old at the time of signing the informed consent and ≤ 75 years old at the time of enrollment. * Patients for Part 1a: patients diagnosed with advanced or recurrent solid tumors. * Patients for Part 1b: patients diagnosed with metastatic NSCLC and confirmed with negative tumor PD-L1 expression (TPS\<1%). * Patients for Part 1b dose expansion study: have never received systemic therapies as primary therapy for advanced or metastatic diseases. * Patients must be able to provide fresh tumor tissues or archived tumor tissues. * 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). * Patients with Eastern Cooperative Oncology Group (ECOG) performance status score ≤ 1. * Patients whose organ function must meet the study requirements. * Males or females with childbearing potential need to use an effective contraceptive method. * Willing and able to comply with study-specified visits schedule, treatment plan, laboratory examination and other study procedures. Exclusion Criteria: * NSCLC patients with EGFR-sensitive mutations or an ALK translocation based on diagnosis results. * Patients who are simultaneously participating in another clinical study, unless the study is an observational (non-interventional) clinical study or the patient is already in the survival follow-up period of the interventional study. * Patients with a medical history of severe allergic diseases, a history of severe drug allergies, and are known or suspected allergy to macromolecular protein preparations or HBM4003 or pembrolizumab excipients. * Previous and concomitant drugs or treatments to be excluded like CTLA4, PD-1,PD-L1. * Insufficient completely recovery from previous treatments. * Diseases that may affect the efficacy and safety of the investigational product. * A history of other malignant diseases within 5 years before the first dose. * Active brain metastasis or leptomeningeal metastasis during screening or previous with imaging evidence (based on CT or MRI assessment). * Patients who have received palliative radiotherapy for non-central nervous system lesions within 2 weeks before the first dose. * Patients who have received more than 30 Gy of lung radiation therapy within 6 months before the first dose. * A history of interstitial lung disease or non-infectious pneumonia. * Patients with pleural effusion, pericardial effusion, or ascites. * Patients that may have other conditions that affect the efficacy or safety evaluation of this study (such as mental disorder, alcoholism, drug abuse, etc.) . * Women who are pregnant or breastfeeding, or who plan to become pregnant during the study period and within 3 months after the last dose of study drug.