The heat transfer process of gold foils irradiated by a femtosecond laser pulse is simulated and studied by the molecular dynamics method combined with the two-temperature model. A local order parameter is adopted to distinguish the solid and liquid phase atoms and the changing laws of the location and temperature of the solid-liquid interface versus time are obtained. On this basis, the effect of laser energy flux density on the melting process is investigated. It is shown that, with the absorption and transfer of laser energy, the lattice arrangement of Au atoms changes gradually from a regular and face-centered-cubic structure into an irregular and loosely arranged one. As time goes by, the solid-liquid interface gradually moves towards the bottom of the gold foil, and the foil volume also expands gradually. When the laser energy flux density is low, the gold foil does not melt completely and the melting is delayed. In contrast, the higher the laser energy flux density is, the melting occurs earlier and more rapidly, the melting depth is larger, and the interfacial temperature is higher.