A progressive geometry compression scheme is presented in this paper. In this scheme, a mesh is represented as a base mesh followed by some groups of vertex split operations using an improved simplification method, in which each level of the mesh can be refined into the next level by carrying out a group of vertex split operations in any order. Consequently, the PM representation can be effectively encoded by permuting the vertex split operations in each group. Meanwhile, a Laplacian geometry predicator is desinged to predict each new verttex position using its neighbors.The correction is quantized and encoded using Huffman coding scheme.Experimental results show that the algorithm can obtain higer compression ratios than than the previous work.It is very suitable for progressive transmission of geometry models over Internet.