Minutiae-based method is the most popular approach in fingerprint matching. However, most existing methods need to search for the best correspondence of minutiae pairs or use reference points (core and delta points) to estimate the alignment parameters. The problem of lost minutiae or spurious minutiae always occurs during the minutiae detection process. Hence, the corresponding pairs or reference points may not be found under this condition. This paper proposes a new minutiae-based fingerprint matching algorithm using phase correlation. We define a new representation called Minutiae Direction Map (MDM). First, we convert minutiae sets into 2D image spaces. Then the transformation parameters are calculated using phase correlation between two MDMs to align two fingerprints to be matched. The similarity of two fingerprints is determined by the distance between two minutiae sets. Our approach does not need to search for the corresponding minutiae pairs. Experimental results show that the proposed approach performed well in matching fingerprint minutiae sets, which greatly improved the economy of storage space.