A phase field model of sintering with direction-dependent interface diffusion is presented, in which the surface and grain boundary diffusions occur along the tangent of surfaces and grain boundaries, respectively. Compared with previous phase field models of sintering, the proposed model is more consistent with the sharp interface model regarding the directions of interface diffusions. Numerical simulations show that the direction of interface diffusion is critical to model sintering kinetics and morphological evolution, and the performance of phase field model is improved significantly with appropriate interface diffusion directions. The proposed model is able to capture relevant features of sintering such as neck growth and its dependence on particle size, interface energies and mobilities. These features agree well with theoretical predictions.