In this work, we present a new approach for the problem of 3D shape correspondence under topological noise. Topological noise can be easily encountered in 3D models acquired by various ways such as motion capture technology. In our proposed approach, the pair of 3D shapes is brought to comparable topology before doing matching. We remove the connections leading to topological changes by moving the shape surface inward along the surface normal with a velocity relative to the curvature at each point. We employ coarse matching under the isometry assumption after bringing the shapes to comparable topology. Our method successfully performed on MIT samba sequence, SHREC10 and SHREC11 datasets.