Utilizing the plane wave expansion method, it is found that there are two types of edge states existing on the surface termination along the ΓM direction of a diatomic photonic crystal. Through analying the surface mode band structure and the field distribution, the effect of the edge parameter on the waveguiding properties of these edge states were investigated. The group index and group velocity dispersion parameter were calculated according to the dispersion curves. The results demonstrate that the variation of the edge parameter has a very slight effect on the light propagation properties of first type of edge state. Its average group index is always around 5.0. The second edge state is obviously different with the first state and the variation of edge parameters can control the propagation performance of this mode efficiently. The maximal average group index of this edge state can achieve 178. The finite difference time domain methods was used to record the electric field distributions and amplitudes near the surface at different times. From the obtained results, it is found that these edge states can be confined in the area near the surface termination and propagate forward. The group velocity extracted from the finite difference time domain method is consistent with the result from the plane wave expansion method.