We present a novel anisotropic surface remeshing method that can efficiently eliminate obtuse angles. Unlike previous work that can only suppress obtuse angles with expensive resampling and Lloyd-type iterations, our method relies on a simple yet efficient connectivity and geometry refinement, which can not only remove all the obtuse angles, but also preserves the original mesh connectivity as much as possible. Our method can be directly used as a post-processing step for anisotropic meshes generated from existing algorithms to improve mesh quality. We evaluate our method by testing on a variety of meshes with different geometry and topology, and comparing with representative prior work. The results demonstrate the effectiveness and efficiency of our approach.