The cell cycle is known to be regulated by features such as the mechanical properties of the surrounding environment and interaction of cells with the adhering substrates. Here, we investigated the possibility of regulating cell-cycle progression of the cells on gelatin/hyaluronic acid composite hydrogels obtained through hydrogen peroxide (H2O2)-mediated cross-linking and degradation of the polymers by varying the exposure time to H2O2 contained in the air. The stiffness of the hydrogel varied with the exposure time. Human cervical cancer cells (HeLa) and mouse mammary gland epithelial cells (NMuMG) expressing cell-cycle reporter Fucci2 showed the exposure-time-dependent different cell-cycle progressions on the hydrogels. Although HeLa/Fucci2 cells cultured on the soft hydrogel (Young’s modulus: 0.20 and 0.40 kPa) obtained through 15 min and 120 min of the H2O2 exposure showed a G2/M-phase arrest, NMuMG cells showed a G1-phase arrest. Additionally, the cell-cycle progression of NMuMG cells was not only governed by the hydrogel stiffness, but also by the low-molecular-weight HA resulting from H2O2-mediated degradation. These results indicate that H2O2-mediated cross-linking and degradation of gelatin/hyaluronic acid composite hydrogel could be used to control the cell adhesion and cell-cycle progression.