Mesh refinement is a powerful technique for representing 3D objects with complex shapes. In this paper, a novel geometric mesh refinement method based on compressed sensing was proposed. The method is motivated by recent advancements in sparse signal reconstruction. The assumption underlying our work is that we can generate high resolution mesh from low resolution mesh by a prior knowledge. After remeshing sample meshes onto a completely regular structure, mesh patches can be represented by the over-complete bases of their own spaces so that their high-level features can be captured by the bases. For the reconstruction model, a prior knowledge about low resolution mesh generation is combined to the typical base construction for high construction quality. So we can get a refined mesh of the input regular low resolution mesh. Our results show that the method can reconstruct high resolution geometric mesh with high quality.