Harmonic current tracking control in harmonic compensation is one of the key factors to measure the performance of active power filter. Aiming at the problem of adjusting linear sliding surface parameters anyway cannot make the tracking error converge to zero in a finite time for ordinary sliding mode control, harmonic current tracking control strategy based on global fast terminal sliding mode control in current loop is proposed. The method introduces nonlinear function based on a linear sliding surface, to make up for shortcomings of ordinary sliding mode control which can achieve gradual convergence of state, while improving the transient performance of the sliding mode control and eliminating the switching term, which essentially weakens the chattering. The steady-state and transient performance tests of active power filter are carried out without changing the harmonic detection link, the comparison between the global fast terminal sliding mode control proposed and the sliding mode control of the conventional exponential approach law verify the correctness and effectiveness of the control strategy proposed .