Faced with serious harmonic pollution, a global fast terminal sliding mode control (GFTSMC) based on a novel recurrent fuzzy neural network (NRFNN) strategy for an active power filter (APF) with uncertainty is proposed in this article, which is aimed at improving the power quality and realizing harmonic suppression. First, the GFTSMC is adopted due to its advantages in finite-time convergence and faster convergence rate of tracking error in the system. Second, NRFNN is adopted to approximate the unknown model and lump the uncertainty of the APF system. Because the values of base width, center vector and feedback gain of NRFNN can be adjusted adaptively according to adaptive laws, the accurate approximation of the unknown model can be achieved, and the robustness and accuracy of the APF system can be guaranteed. Finally, the validity and feasibility of the proposed GFTSMC-NRFNN scheme is fully verified by simulation results, showing it has better steady-state and dynamic performance than other existing methods.