We numerically study the phase behaviors of colloids with anisotropic diffusion in two dimensions.It is found that the diffusion anisotropy of colloidal particles plays an important role in the phase transitions.A strong diffusion anisotropy induces the large vibration of particles,subsequently,the system goes into a disordered state.In the presence of the strong-coupling,particles with weak diffusion anisotropy can freeze into hexagonal crystals.Thus,there exists a solid-liquid transition.With the degree of diffusion anisotropy increasing,the transition points are shifted to the stronger-coupled region.A competition between the degree of diffusion anisotropy and coupling strength widens the transition region where the heterogeneous structures coexist,which results in a broad-peak probability distribution curve for the local order parameter.Our study may be helpful for the experiments related to the phase behavior in statistical physics,materials science and biophysical systems.