The existing automatic mesh simplification algorithms at present always ignore some important shape features of the original model, such as the corners and high-curvature regions, in the low-level model, and this will lead to the degeneration in the sense of sight. On the base of Garland’s simplification algorithm, a method of changing the order of edge collapses in the simplification is presented by introducing the concept of sharp degree into the error metrics. The results can not only preserve the important features of the model but also distribute meshes reasonably. Finally a better simplified model is obtained which has dense meshes in the high-curvature regions and sparse meshes in the flat regions.