Abstract: Two finite difference schemes, the explicit and implicit schemes, were established to solve the one-dimensional melting problem with periodic heat source, while the moving boundary model of the melting problem was transformed to a fixed boundary model by a simple stretching of the spatial coordinate. The numerical stabilities of the explicit and implicit schemes were studied. The computational complexity and efficiency of these two schemes were compared. Also the evolution of the moving boundary and the temperature distribution were simulated numerically by using these two finite difference schemes for the one-dimensional melting problem with periodic heat source. Numerical experiment results showed that the results obtained from these two schemes were in good agreement, but the computational efficiency of the implicit scheme was much higher than that of the explicit scheme