Using the lattice gas model and the transition-type-dependent Monte Carlo method, we calculated the chemical surface diffusion coefficients on a stepped surface. We assume that the step exerts an attraction or repulsion on adsorbed particles (adparticles) that occupy the up or down step sites, but no interactions between adparticles. Two kinds of activation energy, calculated from the harmonic potential and from the difference between the saddle-point and single-site energy, are used in our calculation. The calculated results show that perpendicular diffusion decreases greatly with increase in step repulsion and attraction at all coverages. However, for diffusion parallel to the steps, completely different results are obtained for these two calculation methods. If the energy barrier is calculated by the harmonic potential, diffusion parallel to the steps is both coverage and step independent. If the energy barrier is calculated by the second method, diffusion parallel to the steps is greatly enhanced with increase in the step repulsion and attraction at middle or high coverages but decreases slightly at low coverages. The calculated results explain the chemical diffusion anisotropy on a stepped surface. The results also show that the popular harmonic potential method may be not suitable for explaining the experiments where diffusion along step edges may be more rapid than on a flat surface.