Hepatocellular carcinoma (HCC) is a significant contributor to cancer-related deaths globally. Systemic therapy is the only treatment option for HCC at an advanced stage, with limited therapeutic response. In this study, we evaluated the antitumor potential of four N-acylhydrazone (NAH) derivatives, namely LASSBio-1909, 1911, 1935, and 1936, on HCC cell lines. We have previously demonstrated that the aforementioned NAH derivatives selectively inhibit histone deacetylase 6 (HDAC6) in lung cancer cells, but their effects on HCC cells have not been explored. Thus, the present study aimed to evaluate the effects of NAH derivatives on the proliferative behavior of HCC cells. LASSBio-1911 was the most cytotoxic compound against HCC cells, however its effects were minimal on normal cells. Our results showed that LASSBio-1911 inhibited HDAC6 in HCC cells leading to cell cycle arrest and decreased cell proliferation. There was also an increase in the frequency of cells in mitosis onset, which was associated with disturbing mitotic spindle formation. These events were accompanied by elevated levels of CDKN1A mRNA, accumulation of CCNB1 protein, and sustained ERK1 phosphorylation. Furthermore, LASSBio-1911 induced DNA damage, resulting in senescence and/or apoptosis. Our findings indicate that selective inhibition of HDAC6 may provide an effective therapeutic strategy for the treatment of advanced HCC, including tumor subtypes with integrated viral genome. Further, in vivo studies are required to validate the antitumor effect of LASSBio-1911 on liver cancer.