In view of the problems of the delay of harmonic detection link and bad robustness, tracking accuracy was not high of harmonic current tracking link for Shunt Active Power Filter, the mathematical model of decoupled system was established and global integral sliding mode control for Shunt Active Power Filter based on RLS algorithm was proposed. In harmonic detection link, improved id-iq method of instantaneous reactive power theory was used and the conventional Butterworth low-pass filter was been replaced by RLS adaptive filter to solve the problem of blind-spot detection in a fundamental cycle (20ms) due to the delay of conventional Butterworth low-pass filter. In harmonic current tracking link, global integral sliding mode control was used and the global integral sliding surface was introduced to export the control law taking the rapidity of global sliding and the accuracy of integral sliding into account based on Lyapunov stability theory. In conditions of solving the delay of harmonic detection link, contrasting global integral sliding mode control strategy with traditional PI control and hysteresis control. Simulation experimental results show that the global integral sliding mode control for the command current has higher tracking accuracy and lower current total harmonic distortion of the grid side.