This paper proposes a new mesh simplification algorithm which makes effort in reducing the approximation error and improving the mesh regularity of simplified mesh at the same time. In previous mesh simplification researches, algorithms generally focused on the appearance error between the simplified mesh and the original mesh. However, a so-called high quality simplified mesh must have low approximation error as well as high mesh regularity. According to this consideration, the proposed algorithm extracts the sharp features of original mesh by a normal-based surface clustering scheme before the mesh simplification processing. The extracted features are defined as geometric constraints to reduce the shape distortion caused during the mesh simplification process. In order to improve the regularity of reconstructed base mesh, the proposed algorithm uses the direct resampling scheme combining with the mesh relaxation method to produce a more attractive mesh simplification result than previous mesh simplification algorithms.