The problem of recognizing an individual using minutiae of fingerprints can be considered as a point matching problem. However, several factors such as the translation, rotation and deformation of the fingerprints as well as the presence of spurious minutiae and the absence of genuine minutiae, make it difficult to find correspondent minutia-pairs. In this paper, we proposed a novel topology-based fingerprint matching algorithm named N-layer Delaunay Triangulation Net Check (NDTC). This scheme fully utilizes the advantages of the special features of Delaunay triangulation net, e.g. local structural stability and global structural uniqueness, to tackle these problems, in order to to provide reliable and robust minutiae matching. Our algorithm performance is evaluated on a public domain database FVC2002 DB2_A.