As one of the widely used reactive compensation equipment, the static synchronous compensator (STATCOM) can simultaneously realize the compensation of reactive, harmonic and asymmetric currents. It is difficult to eliminate the steady-state error by using traditional PI controller when STATCOM needs to provide the compensation of harmonic and asymmetric currents. In order to solve these problems, the composite controller model composed of the repetitive and PI controllers is established, which not only fast tracks DC currents, but also significantly accelerates the response speed to AC current. To realize the selective harmonic compensation, a detection approach of reference harmonics based on the dq synchronous reference frame and DFT is proposed and applied to STATCOM. Moreover, based on the combined circuit topology with multi-field programmable gate array (FPGA), the simulation and experiment platform is employed to verify the feasibility and effectiveness of the control strategy.