This paper proposes a neural network based adaptive constrained control scheme for a solid oxide fuel cell (SOFC). First, a radial basis function (RBF) neural network is designed for the identification of SOFC dynamic model. The Jacobian information can be obtained through the identified RBF model. Then, a back propagation (BP) neural network based PID controller is designed to tune the parameters that BP neural network has strong self-learning and adaptive capabilities. At same time, in order to solve the control input saturation and fuel utilization problems of SOFC, a dynamic anti-windup compensator is proposed for accommodating the reference. Moreover this paper theoretically proves the stability of the proposed method based on Lyapunov stability analysis. Finally, the simulation results for SOFC are provided to demonstrate the effectiveness of the proposed constrained control approach. (C) 2016 Elsevier B.V. All rights reserved.