Air compressor of proton exchange membrane fuel cell (PEMFC) system is usually nonlinear and strong coupled. It is difficult to establish a online optimization oriented model. In order to solve this problem, this paper proposed a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model for air compressor of PEMFC system. The NARMAX model is an equivalent time-varying linear model, and the time-varying parameters are identified by recurrent neural network (RNN). Simulation results show that the proposed method has small fitting error, the error of air flow and pressure ratio approximate zero, while the mean square error (MSE) of air flow and pressure ratio are 1.5171e-07 and 6.3767e-05, respectively. Therefore, the established air compressor model is accurate and effective. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.