As the electronic power system develops rapidly, the harmonic problem in the power grid is becoming increasingly serious. To improve the compensation current tracking performance and filtering effect of an active power filter (APF), this paper proposes an improved fractional-order fast terminal sliding mode control (IFOFTSMC) based on tuna swarm optimization (TSO). First, the mathematical model of a three-phase shunt APF is established, and its parameter perturbation is considered. Secondly, an improved fractional-order fast terminal sliding mode control strategy is proposed. In the sliding mode surface, the fractional-order fast terminal sliding mode is combined with fractional-order PI theory, and finite time analysis is presented. Simultaneously, the reaching law combines exponential and power reaching law and takes the arcsinh function as the switching term. Thirdly, the control parameters and order of the designed controller are optimized using the tuna swarm optimization algorithm and the optimal solution is obtained. Finally, the effectiveness of the proposed control method is verified by simulation. In addition, it is further proved that the proposed optimal control algorithm can not only gain the optimal control parameters and fractional order, with the system reaching stability in a finite time, but also makes the APF have better current tracking performance, filtering effect and greater robustness.