In the heat-transfer analysis of a solidification process, the effective specific heat method is conceptually simple to apply while dealing with the latent heat problem. The implementation of computer program is very easy for this method. However, in a time step, if a nodal temperature enters, leaves or jumps over the artificial mushy zone of a pure substance, it cannot calculate the released or absorbed latent heat correctly. If the latent heat is large or the temperature variation is very large, the discontinuity of the effective specific heat will make the iterative convergence difficult to reach. In this work, a modified method is proposed to solve these problems. The method modifies the relation between the temperature and effective specific heat for a solidification process by considering the effect that the temperature at either of two successive time steps is in the mushy zone. The Stefan and Neumann problems with exact solutions were used to test the modified method. The computing results will be compared with those of the effective specific heat method and the enthalpy method. Finally, the feasibility of the modified method is further testified by using a crystal growth problem of GaAs in a Bridgman furnace.