Among cancer-related deaths, hepatocellular carcinoma (HCC) ranks fourth, and traditional Chinese medicine (TCM) treatment is an important complementary alternative therapy for HCC. Curcumin is a natural ingredient extracted from Curcuma longa with anti-HCC activity, while the therapeutic mechanisms of curcumin remain unclear, especially on ferroptosis and cuproptosis.Differentially expressed genes (DEGs) of curcumin treatment in PLC, KMCH, and Huh7 cells were identified, respectively. The common genes among them were then obtained to perform functional enrichment analysis and prognostic analysis. Moreover, weighted gene co-expression network analysis (WGCNA) was carried out for the construction of the co-expression network. The ferroptosis potential index (FPI) and the cuproptosis potential index (CPI) were subsequently used to quantitatively analyze the levels of ferroptosis and cuproptosis. Finally, single-cell transcriptome analysis of liver cancer was conducted.We first identified 702, 515, and 721 DEGs from curcumin-treated PLC, KMCH, and Huh7 cells, respectively. Among them, HMOX1, CYP1A1, HMGCS2, LCN2, and MTTP may play an essential role in metal ion homeostasis. By WGCNA, grey60 co-expression module was associated with curcumin treatment and involved in the regulation of ion homeostasis. Furthermore, FPI and CPI assessment showed that curcumin had cell-specific effects on ferroptosis and cuproptosis in different HCC cells. In addition, there are also significant differences in ferroptosis and cuproptosis levels among 16 HCC cell subtypes according to single-cell transcriptome data analysis.We developed CPI and combined it with FPI to quantitatively analyze curcumin-treated HCC cells. It was found that ferroptosis and cuproptosis, two known metal ion-mediated forms of programmed cell death, may have a vital effect in treating HCC with curcumin, and there are significant differences in various liver cancer cell types and curcumin treatment which should be considered in the clinical application of curcumin.