A shunt hybrid active power filter is proposed for the harmonic problem caused by nonlinear loads in power grid. Based on the topological structure, the mathematical model is established, and the current controller based on PI control strategy is designed. In view of the problem that the compensation accuracy of PI control is not ideal due to the bandwidth constraint, a double closed loop current control method based on repetitive control is proposed, and a double closed loop current controller is designed. Simulation and experimental results show that the proposed control strategy has a high steady-state compensation accuracy, which can effectively restrain the harmonic current caused by nonlinear loads. After compensation, the power grid current THD is reduced to below 5%, and the waveform is close to the sine wave.