The cellular microenvironment plays a critical role in cell differentiation, proliferation, migration, and homeostasis. Recent studies have shown the importance of substrate viscosity in determining cellular function. Here, we study the mechanoresponse of normal hepatocytes and hepatocellular carcinoma cells (HCC) to elastic and viscoelastic substrates using the Huh7 cell line derived from a human liver tumor and primary human hepatocytes (PHH). Unlike PHH and fibroblasts, which respond to viscoelastic substrates by reducing spreading area and actin bundle assembly compared to purely elastic substrates of the same stiffness, Huh7 cells spread faster on viscoelastic substrates than on purely elastic substrates. The steady state spreading areas of Huh7 cells are larger on viscoelastic substrates, whereas the opposite effect occurs with PHH cells. The viscoelasticity of the microenvironment also promotes motility and multiple long protrusions in Huh7 cells. Pharmacologic disruption of the actin assembly makes cells unable to spread on either elastic or viscoelastic substrates. In contrast, upon vimentin perturbation, cells still spread to a limited degree on elastic substrates but are unable to spread on viscoelastic substrates. The time evolution of cell traction force shows that the peak occurs at an earlier time point on viscoelastic substrates compared to elastic substrates. However, the total force generation at steady state is the same on both substrates after 4 hours. Our data suggest that stress relaxation time scales of the viscoelastic substrate regulate cell dynamics and traction force generation, indicating different binding-unbinding rates of the proteins that form cell attachment sites in HCC cells and normal hepatocytes. These results suggest that liver cancer cells may have different characteristic lifetimes of binding to the substrate in comparision to normal cells, which might cause differences in cell spreading and motility within the diseased tissue.