Parameterization of a 3D triangular mesh is a fundamental problem in various applications of geometric modeling and computer graphics. There are two major paradigms in mesh parameterization: energy functional minimization and the convex combination approach. In general, the convex combination approach is wifely used because of simple concept and one-to-one mapping. However, the approach has some problems such as high distortion near the boundary and time complexity. Moreover, the stability of the linear system may not be preserved according to the geometric information of the mesh. In this paper, we present an extension of the convex combination approach based on the mean value coordinates, which resolves the drawbacks of the convex combination approach. This may be a more practical solution because it is able to generate a stable linear system in a short time