The local geometric properties such as curvature and normal vector play important roles in analyzing the local shape of objects. The weighted normal vector methods are applied to estimate the curvatures on surface of meshes. However, these approaches still cause some serious problems, such as when two adjacent triangles are of co-planarity or the shape of triangles of the mesh is irregular. In this paper, we propose an efficient algorithm which is able to compute the normal vectors more accurately and is available to meshes of arbitrary topology. Our method uses the conformal mapping which resembles the local geometric properties synthetically, and the mean value coordinates which may smoothly represent a relationship with the adjacent vertices. It is confirmed by experiment that the normal vector of our algorithm is more accurate than that of the previous methods.