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.