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The aircraft auxiliary power unit (APU) is responsible for environmental control in the cabin and the main engines starting the aircraft. The prediction of its performance sensing data is significant for condition-based maintenance. As a complex system, its performance sensing data have a typically nonlinear feature. In order to monitor this process, a model with strong nonlinear fitting ability needs to be formulated. A neural network has advantages of solving a nonlinear problem. Compared with the traditional back propagation neural network algorithm, an extreme learning machine (ELM) has features of a faster learning speed and better generalization performance. To enhance the training of the neural network with a back propagation algorithm, an ELM is employed to predict the performance sensing data of the APU in this study. However, the randomly generated weights and thresholds of the ELM often may result in unstable prediction results. To address this problem, a restricted Boltzmann machine (RBM) is utilized to optimize the ELM. In this way, a stable performance parameter prediction model of the APU can be obtained and better performance parameter prediction results can be achieved. The proposed method is evaluated by the real APU sensing data of China Southern Airlines Company Limited Shenyang Maintenance Base. Experimental results show that the optimized ELM with an RBM is more stable and can obtain more accurate prediction results.