Melting phenomenon is accompanied with phase change. Hence we introduce in ordinary theory of heat conduction latent of fusion, and obtain numerical solutions of one-dimentional non-liner differential equations under various conditions for such a theory. As results, it becomes clear that the effect of latent heat of fusion is relatively large, especially discrepancy of size of melting region by ordinary theory from by our theory is important, for example in non-stationary melting of Al it amounts to nearly 40% under some conditions.