Fingerprint distortion changes both the geometric position and orientation of minutiae, and leads to difficulties in establishing a match among multiple impressions acquired from the same finger. In this paper, minutia polygons are used to match distorted fingerprints. A minutia polygon describes not only the minutia type and orientation but also the minutia shape. This allows the minutia polygon to be bigger than the conventional tolerance box without losing matching accuracy. In other words, a minutia polygon has a higher ability to tolerate distortion. Furthermore, the proposed matching method employs an improved distortion model using a Multi-quadric basis function with parameters. Adjustable parameters make this model more suitable for fingerprint distortion. Experimental results show the proposed method is two times faster and more accurate (especially, on fingerprints with heavy distortion) than the method in [1].