Coping with nonlinear distortions in fingerprint matching is a challenging task. This paper proposes a novel algorithm, normalized fuzzy similarity measure (NFSM), to deal with the nonlinear distortions. The proposed algorithm has two main steps. First, the template and input fingerprints were aligned. In this process, the local topological structure matching was introduced to improve the robustness of global alignment. Second, the method NFSM was introduced to compute the similarity between the template and input fingerprints. The proposed algorithm was evaluated on fingerprints databases of FVC2004. Experimental results confirm that NFSM is a reliable and effective algorithm for fingerprint matching with nonliner distortions. The algorithm gives considerably higher matching scores compared to conventional matching algorithms for the deformed fingerprints.