This article focuses on the design of a terminal sliding mode control (TSMC) using a fuzzy double hidden layer recurrent neural network (FDHLRNN) strategy for a single-phase active power filter (APF). A TSMC is proposed to make the tracking error of the system converge to zero in a finite time. An FDHLRNN is proposed and applied in harmonic suppression to approximate the equivalent control and eliminate the unknown disturbance, reducing the role of symbol switching items. The main function of the FDHLRNN is to improve control accuracy and reduce the current distortion rate of the APF. The designed FDHLRNN is the weighted sum of the fuzzy network and the double hidden layer network, having a strong global learning ability. The adaptive parameters of the FDHLRNN are derived by the Lyapunov function to ensure the asymptotic stability of the system. The compensation performance and effectiveness of the proposed TSMC using FDHLRNN strategy are verified by real-time experiments.