This paper presents an accurate method for computing the surface velocity which is used to advect the vertex in mesh-based surface tracking. We propose a curvature invariance condition that accurately captures the movement of a surface, especially in the case of rotating objects. The method uses the least-squares method and mesh fairing to solve the problem that the surface velocity would not be calculated when the implicit function defining the surface does not change. We show that the method works well in scenes including rotation and deformation.