In order to achieve accurate current tracking control, an active power filter fractional-order fast terminal sliding mode control method based on a self-organizing recurrent emotional neural network (SORENN) is proposed. Firstly, a fractional-order fast terminal sliding mode controller (FOFTSMC) is designed for an active power filter system. Because fractional-order introduces more degrees of freedom, the system is more adaptable and robust. Secondly, a novel brain-like neural network SORENN based on the brain emotion learning model and peak self-organization mechanism is constructed and introduced to solve the problem that the fractional- order fast terminal sliding mode controller depends on precise system parameters, thereby improving its control performance. At the same time, compared with other general neural networks, the SORENN solves the problem that ordinary neural networks cannot update the network structure online due to the addition of the peak self-organization mechanism, realizes the online optimization of the network structure, reduces the computing burden, and improves the learning rate and approximation ability of the network. Then, the stability and convergence of this control method are proved according to the Lyapunov stability theorem. Finally, through many simulation and experimental studies on the hybrid intelligent control method, its excellent control performance is revealed.