Most clinical and experimental studies have suggested that hepatitis C virus (HCV) is dominant over hepatitis B virus (HBV) during coinfection, although the underlying mechanism remains unclear. In this study, we found that the HBV X protein (HBx) upregulates the levels of the HCV core protein to stimulate HCV replication during coinfection in human hepatoma cells. For this purpose, HBx upregulated both the protein levels and enzyme activities of cellular DNA methyltransferase 1 (DNMT1) and DNMT3b, and this subsequently reduced the expression levels of the E6-associated protein (E6AP), an E3 ligase of the HCV core protein, via DNA methylation. The ubiquitin-dependent proteasomal degradation of the HCV core protein was severely impaired in the presence of HBx, whereas this effect was not observed when E6AP was either ectopically expressed or restored by treatment with 5-aza-2'dC or DNMT1 knockdown. The effect of HBx on the HCV core protein was accurately reproduced in HBV/HCV coinfection systems, which were established by either monoinfection by HCV in Huh7D cells transfected with a 1.2-mer HBV replicon or coinfection by HBV and HCV in Huh7D-Na+-taurocholate cotransporting polypeptide cells, providing evidence for the stimulation of HCV replication by HBx. The present study may provide insights into understanding HCV dominance during HBV/HCV coinfection in patients. IMPORTANCE Hepatitis B virus (HBV) and hepatitis C virus (HCV) are major human pathogens that cause a substantial proportion of liver diseases worldwide. As the two hepatotropic viruses have the same modes of transmission, coinfection is often observed, especially in areas and populations where HBV is endemic. High-risk populations include people who inject drugs. Both clinical and experimental studies have shown that HCV is more dominant than HBV during coinfection, but the underlying mechanism remains unclear. In this study, we show that HBV X protein (HBx) stimulates HCV replication by inhibiting the expression of E6-associated protein (E6AP) via DNA methylation, thereby protecting the HCV core protein from proteasomal degradation, which can contribute to HCV dominance during HBV/HCV coinfection.