Inclusion Criteria:  Ability to provide written and signed informed consent. Age ≥ 18 years at time of study entry Histologically or cytologically confirmed recurrent or metastatic high grade neuroendocrine carcinoma of the cervix with disease progression confirmed by radiologic imaging during or following prior platinum-based doublet chemotherapy, with or without bevacizumab for recurrent or metastatic cervical cancer Received no more than 3 prior systemic therapies in the recurrent or metastatic setting Not eligible for surgery and/or radiation as treatment options for recurrent disease Measurable lesions according to RECIST v1.1. (A previously irradiated lesion is not considered measurable and cannot be selected as a target lesion.) Eastern Cooperative Oncology Group performance status (ECOG PS) score of 0 or 1  Adequate organ function as determined by:  Hematological criteria (subjects should not have received either growth factor support or recent transfusions within 7 days prior to starting study treatment):  Absolute neutrophil count (ANC) ≥1.5 × 109  /L (1,500/mm3  Platelet count ≥100 × 109  /L (100,000/mm3  Hemoglobin ≥9.0 g/dL (90 g/L)  Renal criteria:  - Serum creatinine <1.5 × upper limit of normal (ULN), or estimated glomerular filtration rate (eGFR) ≥45 mL/min/1.73 m 2 by Cockcroft-Gault formula  Hepatic criteria:  AST and ALT ≤2.5 × ULN; for subjects with liver metastasis, AST/ALT can be  ≤5 × ULN  Serum total bilirubin (TBL) ≤1.5 × ULN; for subjects with documented/suspected Gilbert's disease, TBL <3 × ULN  One of the following conditions applies:  Is a woman of childbearing potential (WOCBP) who is sexually active with a nonsterilized male partner must have a negative pregnancy test at the Screening visit (within 3 days prior to the first dose of the investigational product [Cycle 1 Day 1]), should not be lactating, and must agree to use 1 methods of contraception Is a woman of nonchildbearing potential Willing and able to comply with scheduled visits, treatment plan, laboratory tests, and other study procedures as specified in the protocol  Exclusion Criteria:  Concurrent enrollment in another clinical study, unless it is an observational (noninterventional) clinical study or the follow-up period of an interventional study  Histological types of cervical cancer other than high grade neuroendocrine caricnoma (e.g.  squamous carcinoma, adenocaricnoma, adeno-squamous carcinoma, clear cell carcinoma, sarcoma, etc.)  Prior malignancy active within the previous 2 years except for the tumor for which a subject is enrolled in the study and locally curable cancers that have been apparently cured, such as basal cell skin cancer or carcinoma in situ of the breast Brain/central nervous system (CNS) metastases: Subjects with suspected brain metastases should have a computed tomography (CT)/magnetic resonance imaging (MRI) scan of the brain to confirm the absence of brain/CNS metastases prior to enrollment. Clinically significant hydronephrosis, as determined by the investigator, not alleviated by nephrostomy or ureteral stent Active infections (including tuberculosis) requiring systemic antibacterial, antifungal, or antiviral therapy within 4 weeks prior to the first dose of investigational product. Known history of testing positive for human immunodeficiency virus (HIV) or known active acquired immunodeficiency syndrome. Known active hepatitis B or C infections (known positive hepatitis B surface antigen [HBsAg] result or positive hepatitis C virus [HCV] antibody with detectable HCV ribonucleic acid [RNA] results). Active or prior documented autoimmune disease that may relapse. NOTE: Subjects with controlled type 1 diabetes mellitus, thyroiditis in euthyroid state or hypothyroidism well managed by hormone replacement therapy (HRT), or skin diseases not requiring systemic treatment (e.g., vitiligo, psoriasis) are eligible. History of interstitial lung disease or noninfectious pneumonitis, except for those induced by radiation therapies.  Clinically significant cardio-cerebrovascular disease:  Myocardial infarction, unstable angina, pulmonary embolism, stroke, or any other significant cardiovascular or cerebrovascular accident within 6 months prior to the first dose of investigational product. New York Heart Association Grade III or greater congestive heart failure within 6 months prior to the first dose of investigational product. Serious cardiac arrhythmia such as ventricular arrhythmia requiring medication or second- or third-degree atrioventricular block. This does not include asymptomatic atrial fibrillation with controlled ventricular rate. Unresolved toxicities from prior anticancer therapy, defined as having not resolved to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) v5.0 Grade 0 or 1, or to levels dictated in the eligibility criteria with the exception of toxicities not considered a safety risk (e.g., alopecia, neuropathy, or asymptomatic laboratory abnormalities). History of severe hypersensitivity reactions to other mAbs. Prior allogeneic stem cell transplantation or organ transplantation. Known allergy or reaction to any component of the AK104 formulation.  Receipt of the following treatments or procedures:  Anticancer small-molecule targeted agent within 2 weeks prior to the first dose of investigational product. Radiation therapy within 2 weeks prior to the first dose of investigational product. Other anticancer therapy (e.g., chemotherapy, radiotherapy, anticancer mAbs, etc) within 4 weeks prior to the first dose of investigational product. Any major surgery (e.g., laparotomy, thoracotomy, removal of organ[s]) within 4 weeks prior to the first dose of investigational product. Any other nonapproved investigational product or procedure within 4 weeks prior to the first dose of investigational product. Agents with immunomodulatory effect (e.g., thymosin, IFN, interleukin) within 2 weeks prior to the first dose of investigational product.  Subjects with a condition requiring systemic treatment with either corticosteroids (>10 mg daily doses of prednisone or equivalent) or other immunosuppressive medications within 14 days prior to the first dose of investigational product. The following are exceptions to this criterion:  Corticosteroids used as adrenal replacement (<10 mg daily prednisone or equivalent). Topical, ocular, intra-articular, intranasal, or inhaled corticosteroids with minimal systemic absorption. Corticosteroids used as pretreatment medication for hypersensitivity reactions (e.g., CT scan premedication). Receipt of live attenuated vaccines within 30 days prior to the first dose of investigational product. Note: Seasonal vaccines for influenza which are generally inactivated are allowed. Prior exposure to any experimental antitumor vaccines, or any agent targeting T-cell costimulation or immune checkpoint pathways (e.g., anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4, anti-CD137 or anti-OX40 antibody, etc). Any condition that, in the opinion of the Investigator, would interfere with evaluation of the investigational product or interpretation of subject safety or study results.