Literature has shown that radiotherapy can promote tumor antigen presentation, mobilize and activate T cells by enhancing activation signals and blocking inhibitory signals. It can also lead to the normalization of blood vessels in the tumor microenvironment and the increase of CXCL16 and other chemokines to activate T cells. The cells infiltrate the tumor tissues better and promote the killing activity of T cells. Therefore, the combined application of radiotherapy and immunotherapy may have a synergistic effect. Apatinib is a small molecule tyrosine protein kinase inhibitor for VEGFR. Low-dose apatinib can induce the normalization of abnormal blood vessels in tumors, effectively increase the infiltration of lymphocytes in tumor tissues, and block immunosuppressive myeloid cells. Recruitment, reverse the immunosuppressive state, effectively reduce the level of TGF-β, and make the tumor environment tend to have an immune support phenotype. Apatinib combined with PD-1 antibody karelizumab has been confirmed in a phase I study to have good efficacy and safety in patients with advanced liver cancer. Therefore, this study intends to use the PD-1 antibody carrelizumab combined with apatinib and radiotherapy to treat patients with advanced liver cancer with extrahepatic metastasis, to evaluate the effectiveness and safety of the combined therapy, and to provide new clinical treatments for liver cancer Evidence-based medicine.

Inclusion Criteria:

1. Age: ≥18 years old, male or female; 2. Patients with hepatocellular carcinoma diagnosed by imaging examination or pathology; 3. Not suitable for surgical resection or local treatment, patients with lymph or lung metastasis; 4.Child-Pugh score: Grade A, normal liver volume (liver volume-gross tumor volume) > 700 ml; 5. The ECOG score is 0-1 within one week before entering the group; 6. There is at least one measurable lesion that meets the mRECIST and RECIST 1.1 standards; 7. The expected survival time is ≥3 months; 8. The main organs function normally, that is, they meet the following standards:

1. routine blood examination: no blood transfusion, no G-CSF, no drug correction within 14 days before screening) Hb ≥90g/L, ANC ≥1.5×109/L, PLT ≥50×109/L, WBC ≥2.5×109/L ..
2. creatinine ≤1.5ULN. 9. Patients with active hepatitis B virus (HBV) infection: HBV-DNA < 2000IU/ml (if the research center has only copy/mL detection unit, it must be < 104Copy/ml), and receive antiviral treatment before and during the treatment; Patients with hepatitis c virus (HCV) RNA positive: HCV-RNA < 103/ml, must receive antiviral treatment according to local standard treatment guidelines, and the liver function is increased within ctcae grade 1.

10. Women of childbearing age (generally 15-49 years old) must have a negative pregnancy test (serum or urine) within 14 days before entering the group, and voluntarily adopt appropriate methods of contraception during the observation period and within 8 weeks after the last administration of research drugs; For men, they should be sterilized by surgery or agree to use appropriate methods of contraception during the observation period and within 8 weeks after the last administration of study drugs.

11. The subjects voluntarily joined the study, signed the informed consent form, and had good compliance and cooperated with the follow-up.

Exclusion Criteria:

1. Those with a history of esophageal and gastric variceal bleeding, hepatic encephalopathy, massive ascites and abdominal infection.
2. Patients with known history of allogeneic organ transplantation or allogeneic hematopoietic stem cell transplantation or planned transplantation;
3. Previously used immunosuppressive drugs within 14 days before the first use of Karelizumab, excluding nasal spray and inhaled corticosteroids or systemic steroid hormones with physiological dose (i.e. prednisolone or other corticosteroids with the same physiological dose);
4. It is known to be allergic to apatinib, kareli zumab or pharmaceutical excipients; Or severe allergic reaction to other monoclonal antibodies;
5. Vaccinate live attenuated vaccine within 4 weeks before the first administration or during the study period;
6. There are peripheral neuropathy of grade > 1;
7. Any other malignant tumor that has been diagnosed, except basal cell or squamous cell skin cancer or cervical carcinoma in situ that has been fully treated;
8. Human immunodeficiency virus (HIV) infection or known acquired immunodeficiency syndrome (AIDS);
9. Within 6 months before entering the study, the following conditions occurred: myocardial infarction, severe/unstable angina pectoris, NYHA 2 or above cardiac insufficiency, arrhythmia with poor control (including QTcF interval > 450 ms for men and > 470 ms for women, QTcF interval calculated by Fridericia formula), symptomatic congestive heart failure;
10. Hypertension patients with uncontrollable drugs;
11. Abnormal coagulation function (INR>1.5 or APTT>1.5×ULN), bleeding tendency or being treated with thrombolytic therapy, anticoagulant therapy or antiplatelet therapy, etc.;
12. It is known that there are hereditary or acquired bleeding and thrombotic tendencies, such as hemophilia, coagulation dysfunction, thrombocytopenia, hypersplenism, etc.;
13. There is obvious cough blood within 2 months before entering the study, or the daily cough blood volume reaches half a teaspoon (2.5 ml) or more;
14. Patients with gastrointestinal bleeding risk, including the following:

(1) Active peptic ulcer lesions; (2) Those who have a history of black stool and hematemesis within 3 months; (3) For fecal occult blood (+) or (+/-), it needs to be reviewed within 1 week, and gastroscopy should be performed if it is still (+) or (+/-). If there is ulcer or hemorrhagic disease, and the attending doctor thinks there is potential bleeding risk; 15. Arterial/venous thrombosis events occurred within 6 months before entering the study, such as cerebrovascular accidents (including temporary ischemic attack, cerebral hemorrhage and cerebral infarction), deep venous thrombosis and pulmonary embolism, etc.; 16. Infections requiring drug intervention within 4 weeks before the first administration (such as intravenous drip of antibiotics, antifungal or antiviral drugs), or fever of unknown cause > 38.5°C； during screening/before the first administration; 17. Participated in any other drug clinical research within 4 weeks before the first administration; 18. It is known that there is a history of psychotropic drug abuse or drug abuse; 19. There are other serious physical or mental diseases or abnormal laboratory examination, which may increase the risk of participating in the study, or interfere with the results of the study, and the researchers think that the patients are not suitable for participating in the study.