Within the framework of the sintering process simulation, this paper proposes a numerical strategy for the direct simulation of the matter transport by surface diffusion. A level-set method is used to describe the topological changes which arise at the free boundary of the sintering particles. The surface velocity is found to be proportional to the surface Laplacian of the curvature, that is, proportional to the fourth-order derivative of the level-set function. Consequently, both curvature and velocity must be computed carefully and with accuracy. Finally, three-dimensional simulations are shown and investigated.