Fingerprint classification is an effective technique for reducing the candidate numbers of fingerprints in the stage of matching in automatic fingerprint identification system (AFIS). In recent years, deep learning is an emerging technology which has achieved great success in many fields, such as image processing, natural language processing and so on. In this paper, we only choose the orientation field as the input feature and adopt a new method (stacked sparse autoencoders) based on depth neural network for fingerprint classification. For the four-class problem, we achieve a classification of 93.1 percent using the depth network structure which has three hidden layers (with 1.8% rejection) in the NIST-DB4 database. And then we propose a novel method using two classification probabilities for fuzzy classification which can effectively enhance the accuracy of classification. By only adjusting the probability threshold, we get the accuracy of classification is 96.1% (setting threshold is 0.85), 97.2% (setting threshold is 0.90) and 98.0% (setting threshold is 0.95). Using the fuzzy method, we obtain higher accuracy than other methods.