Three surface diffusion models were proposed in our simulation study of the growth of an NaCl type crystal. Our results indicate that the involvement of surface diffusion enhances the rate of growth drastically and gives a relative short nucleation dip. However the more physically meaningful model among these three, which considers the differences in activation barrier along the lateral and diagonal directions, causes an intermediate enhancement of the growth rate. In general, the rate enhancement depends on the number of allowed surface diffusion paths. Competition of diffusion jumps of various kinds as described in these models is expected in reality.