We propose a novel approach to classify fingerprints using the extracted adaptive core block for improving classification performance of incomplete fingerprints in this paper. We compute representative directions from fingerprint images by the block unit and learn horizontal and vertical Markov models by deciding the center position of a fingerprint image based on the expert knowledge. The center block of a test image is the block has the highest probability after comparing the Markov model with $11{ imes}11$ blocks. The proposed approach can effectively classify incomplete fingerprints using the optimal center block.