This paper proposes novel topology-based algorithms for fingerprint matching. Three major aspects of fingerprint matching are considered: local matching, tolerance to deformation and global matching. The approach improves both the accuracy and the speed of fingerprint identification. Computational geometry methods including Delaunay triangulation and spatial interpolation are used. The proposed methods are able to efficiently deal with the distortions of fingerprints. Experimental results confirm that the algorithms presented are effective and more efficient compared to other fingerprint matching algorithms.