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In this paper, a new non-linear distortion robust fingerprint feature named Minutiae Phase Difference Feature (MPDF) is proposed, and used to measure the similarity of fingerprint local structures. Then a novel minutiae expanding method based on Moving Least Squares (MLS) transformation is introduced to regain the lost matched minutiae pairs after obtaining a few valid pairs. Finally a score evaluation strategy based on convex hull of transformed minutiae is adopted, which is more reasonable for partial overlapping fingerprint. Experiments of proposed algorithm conducted on FVC2004 database, comparing with other matching methods, show that the MPDF feature and proposed algorithm have promising performances.