This paper presents a method for dividing the triangle mesh into n-edge mesh and puts forward a new mesh simplification algorithm based on n-edge mesh collapse. An n-edge mesh can be in the form of an edge, a triangle or a quadrangle, it depends on the value of ‘n’. The algorithm utilizes iterative collapse of n-edge mesh to simplify meshes and the surface error approximations are maintained using quadric error metrics. There are n-1 vertices and 2(n-1) faces which have to be collapsed during every simplification, so only few collapses are need when n becomes bigger. And this means, the time of the simplification process can be reduced. Our algorithm contains Garland’s (n=2) [5] and Pan’s (n=3) [11] cases, thus it can be regarded as the summarized algorithm of mesh simplification based on the geometry element collapse. Experimental results demonstrate the different cases, which hold different values of ‘n’ in the algorithm.