DNA methylation is a widespread epigenetic signal in human genome. With Nanopore technology, differential methylation modifications including 5-methylcytosine (5mC) and 6-methyladenine (6mA) can be identified. 5mC is the most important modification in mammals, although 6mA may also function in growth and development as well as in pathogenesis. While the role of 5mC at CpG islands in promoter regions associated with transcriptional regulation has been well studied, but the relationship between 6mA and transcription is still unclear. Thus, we collected two pairs of tumor tissues and adjacent normal tissues from hepatocellular carcinoma (HCC) surgical samples for Nanopore sequencing and transcriptome sequencing. It was found that 2,373 genes had both 5mC and 6mA, along with up- and down-regulated methylation sites. These genes were regarded as unstable methylation genes. Compared with 6mA, 5mC had more inclined distribution of unstable methylation sites. Chi-square test showed that the levels of 5mC were consistent with both up- and down-regulated genes, but 6mA was not significant. Moreover, the top three unstable methylation genes, TBC1D3H, CSMD1, and ROBO2, were all related to cancer. Transcriptome and survival analyses revealed four potential tumor suppressor genes including KCNIP4, CACNA1C, PACRG, and ST6GALNAC3. In this study, we firstly proposed to combine 5mC and 6mA methylation sites to explore functional genes, and further research found top of these unstable methylation genes might be functional and some of them could serve as potential tumor suppressor genes. Our study provided a new solution for epigenetic regulation research and therapy of HCC.