[Objective] To address the current tracking challenges in the harmonic suppression of active power filters （APF）， a fast integral terminal sliding mode control （FITSMC） strategy based on a hippocampus-based fuzzy neural network （HBFNN） is proposed. [Methods] The FITSMC is employed to guarantee global robustness and finite-time convergence of the tracking error. To circumvent the dependence on accurate system parameters， the HBFNN is constructed to approximate unknown system dynamics online. By integrating the hippocampus mechanism with fuzzy theory， the HBFNN eliminates redundancy through feature selection and enhances anti-interference performance against time-varying signals via a double recurrent structure. [Results] Simulation and hardware experiments verify that the proposed HBFNN-FITSMC scheme tracks harmonic currents rapidly and accurately. In simulations， the total harmonic distortion （THD） of the grid-side current decreases from 40.30% to 1.25%， while in hardware experiments， it decreases from 32.73% to 2.96%. Compared with traditional methods， the proposed strategy significantly improves dynamic response and steady-state accuracy， while effectively suppressing system chattering. [Conclusion] By virtue of its information screening and double recurrent mechanism， the HBFNN demonstrates superior approximation and anti-interference capabilities， reducing reliance on precise mathematical models. This scheme achieves the complementary advantages of brain-inspired intelligence and sliding mode control， offering significant value for engineering applications.