The dense correspondence of 3D facial surface is the premise and foundation of 3D face analysis. The majority of the techniques deform a template to fit the target, and the non-rigid iterative closest point (ICP) is the most widely used one, this method fits high-resolution 3D facial template mesh to 3D target face (scan face data) step by step. But this type of methods maintain the topology of the edge regions at the expense of edge precision, in order to ensure the dense correspondent between deformed faces. Aiming at this problem, a non-rigid iterative closed point algorithm combining topological structure loss was proposed, which keeps the topology of the facial edge regions without sacrificing the registration accuracy. Experiments show that our algorithm perform better than the state of art.