This article proposes an adaptive dynamic terminal sliding mode control (ADTSMC) based on a finite-time disturbance observer (FTDO) for a single-phase active power filter (APF). Aiming at the internal parameter fluctuations and external unknown disturbances in the APF system, an FTDO is designed to compensate for the unknown uncertainties. Then, the proposed dynamic terminal sliding mode control (DTSMC) method combines the dynamic sliding mode control and the terminal sliding mode control to achieve finite-time convergence and weaken system chattering. In order to ensure the organic combination of FTDO and DTSMC, a dual-hidden-layer recurrent neural network (DHLRNN) is used to estimate the gain of sliding mode switching term adaptively so that FTDO can achieve the maximum disturbance estimation. Hardware experiments verify that the designed ADTSMC method has satisfactory robustness and harmonic compensation property under different nonlinear loads.