Fingerprints are most widely used for personal identification. It is very important to detect singular points (core and delta) accurately and reliably in most fingerprint verification and identification algorithms for locating reference points for minutiae matching and classification. In this paper, we propose a new adaptive algorithm for singular points detection, which is based on the distribution of Gaussian-Hermite moments of different orders of the fingerprint image. Experimental results show that the proposed algorithm is able to locate singular poins in fingerprint with high accuracy.