Passenger profiling plays a vital part of commercial aviation security, but classical methods become very inefficient in handling the rapidly increasing amounts of electronic records. This paper proposes a deep learning approach to passenger profiling. The center of our approach is a Pythagorean fuzzy deep Boltzmann machine (PFDBM), whose parameters are expressed by Pythagorean fuzzy numbers such that each neuron can learn how a feature affects the production of the correct output from both the positive and negative sides. We propose a hybrid algorithm combining a gradient-based method and an evolutionary algorithm for training the PFDBM. Based on the novel learning model, we develop a deep neural network (DNN) for classifying normal passengers and potential attackers, and further develop an integrated DNN for identifying group attackers whose individual features are insufficient to reveal the abnormality. Experiments on data sets from Air China show that our approach provides much higher learning ability and classification accuracy than existing profilers. It is expected that the fuzzy deep learning approach can be adapted for a variety of complex pattern analysis tasks.