Towards contactless and low cost 3D fingerprint reconstruction, a feature matching method is proposed in this paper, which includes four steps such as preprocessing, feature extraction, matching and postprocessing. In the preprocessing step, touchless fingerprint image is segmented from background according to the color of skin, and it is enhanced in parallel based on STFT and Retinex to increase the contrast of ridges and valleys. Then, ridge map is extracted through binarizing the enhanced fingerprint image and thinning the ridges to one pixel width, and it is filtered with a minutiae template taken by touched fingerprint minutiae extraction methods generally to obtain minutia. In the matching step, a minutiae descriptor is established according to the histogram of oriented gradient of nine sub-regions, on the basis of the similarity of which minutia are matched, and the ridges where corresponding minutia located are also matched guiding by minutiae correspondences. Finally, several constrains such as fingerprint types, relative position, are used to remove false correspondences. Experiment results show that the presented algorithm performs well on minutiae matching even with the low ridge-valley contrast of contactless fingerprint images, and ridge matching also can achieve good results though there are several false matches due to the differences between extracted ridge maps.