Mesh simplification is an important research topic in scientific visualization and virtual reality. The simplification metric is a key issue of a simplification algorithm. In this study, two new simplification metrics based on surface moments and volume moments are proposed, which take the difference between the moments defined by the original mesh and those of the simplified mesh as the objective function. These metrics were used in an edge collapse scheme in order to prove their usability in the mesh simplification procedure. For a given maximum order and the number of triangles required, the optimal mesh with a minimum moment difference from the original mesh can be determined. The procedures are applied to some models and better results are obtained in comparison with some known algorithms.