A geometry-driven hierarchical compression technique for triangle meshes is proposed such that the compressed 3D models can be efficiently transmitted in a multi-resolution manner. In 3D progressive compression, we usually simplify the finest 3D model to the coarsest mesh vertex by vertex and thus the original model can be reconstructed from the coarsest mesh by operating vertex-split operations in the inversed vertex simplification order. In general, the cost for the vertex-split operations will be increased as the mesh grows. In this paper, we propose a hierarchical compression scheme to keep the cost of the vertex-split operations being independent to the size of the mesh. In addition, we propose a geometry-driven technique, which predicts the connectivity relationship of vertices based on their geometry coordinates, to compress the connectivity information efficiently. The experimental results show the efficiency of our scheme.