Abstract Background Cuproptosis, a newly discovered mode of cell death, has been less studied in hepatocellular carcinoma (HCC). Exploring the molecular characteristics of different subtypes of HCC based on cuproptosis-related genes (CRGs) is meaningful to HCC. In addition, immunotherapy plays a pivotal role in treating HCC. Exploring the sensitivity of immunotherapy and building predictive models are critical for HCC. Methods The 357 HCC samples from the TCGA database were classified into three subtypes, Cluster 1, Cluster 2, and Cluster 3, based on the expression levels of ten CRGs genes using consensus clustering. Six machine learning algorithms were used to build models that identified the three subtypes. The molecular features of the three subtypes were analyzed and compared from some perspectives. Moreover, based on the differentially expressed genes (DEGs) between Cluster 1 and Cluster 3, a prognostic scoring model was constructed using LASSO regression and Cox regression, and the scoring model was used to predict the efficacy of immunotherapy in the IMvigor210 cohort. Results Cluster 3 had the worst overall survival compared to Cluster 1 and Cluster 2 (P = 0.0048). The AUC of the Catboost model used to identify Cluster 3 was 0.959. Cluster 3 was significantly different from the other two subtypes in gene mutation, tumor mutation burden, tumor microenvironment, the expression of immune checkpoint inhibitor genes and N⁶-methyladenosine regulatory genes, and the sensitivity to sorafenib. We believe Cluster 3 is more sensitive to immunotherapy from the above analysis results. Therefore, based on the DEGs between Cluster 1 and Cluster 3, we obtained a 7-gene scoring prognostic model, which achieved meaningful results in predicting immunotherapy efficacy in the IMvigor210 cohort (P = 0.013). Conclusions Our study provides new ideas for molecular characterization and immunotherapy of HCC from machine learning and bioinformatics. Moreover, we successfully constructed a prognostic model of immunotherapy.