In this paper, a robust nonsingular fast converging sliding mode control (RNFCSMC) with particle swarm optimization (PSO)-based radial basis function (RBF) neural network is presented and applied in hydrogen fuel cell systems capable to maintain low harmonic distortion even in case of nonlinear load. The proposed technical method is a modified structure: a RNFCSMC plus a PSO-based RBF neural network. Though the classic sliding mode control has inherent robustness against plant parameter variations and load disturbances, the convergence of the system states to the zero is usually asymptotical in infinite time. The RNFCSMC is introduced to assure the finite time convergence of the system states and there is no singularity problem. But, once a severe load disturbance is applied, the chattering or steady-state error still exists in RNFCSMC. The PSO-based RBF neural network is employed to determine the control gains of the RNFCSMC, thus eliminating the chattering or steady-state error so that the system performance reaches the optimal point. The proposed technical method has been realized (1 kW, 110V(rms)/60 Hz) for the actual single-phase hydrogen fuel cell inverters controlled by a TI DSP. Simulation and experimental results reveal that even under nonlinear load circumstances the proposed technical method yields voltage total harmonic distortion (THD) less than 1.4%, which excels the IEEE standard 519, thus demonstrating the effectiveness of the proposed technical method. Because the proposed hydrogen fuel cell system is considerably simpler to implement than classic sliding mode system and offers faster computational speed, this paper will be a beneficial reference to related control designers of hydrogen fuel cell systems. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.