Abstract: This paper presents a new robust multi-level partition of unity (MPU) method, which constructs an implicit surface from a triangular mesh via the new error metric between the mesh and the implicit surface. The new error metric employs a weighted function of inner points and vertices of a triangle to fit an implicit surface, which can control the approximation error between the surface and vertices of the triangle. Furthermore, it is applied to the MPU method by utilizing the dual graph of a triangular mesh, and the general quadric implicit surface is used for surface representation. Compared with the MPU method, the new method generates fewer subdivision cells with the same approximation error and performs more steadily especially when given triangular mesh with fewer vertices.