The surface simplification of point-sampled geometry is one of the key preprocessing techniques for subsequent modeling and visualization algorithms. Based on geometry images, in the paper, we put forward a novel simplification algorithm for pointsampled surfaces. First the point-sampled surfaces are represented as geometry images by projecting their spherical polar coordinates onto a plane. Based on geometry images, the k-nearest neighbors of sample points are then determined significantly fast and their curvatures are estimated. Finally, the point set surfaces are simplified according to the curvature and simplified density. In addition, the quality of the simplified point set surfaces is evaluated using the error measurement method based on the moving least squares surface. This algorithm is very fast, easy to implement and can create high-quality surface approximation with preserving the detail very well and control the simplified density conveniently.