The three-phase shunt active power filter（SAPF）is taken as the research objective in this paper and the traditional compound current control strategy combining PI and repetitive control（RC）is analyzed firstly. The repetitive controller in this strategy will amplify high-frequency harmonics while achieving high-precision tracking of periodic sinusoidal signals

which has effect on the compensation result.Therefore

an improved repetitive controller based on discrete Fourier transform（DFT）is proposed. The improvement of structure can not only compensate specific harmonics

but also have a faster response speed.Therefore

the compound controller cascaded with PI has superior steady-state performance and dynamic characteristics. Finally

the effectiveness of the proposed strategy is verified by Matlab simulation results.