In view of active power filter’s control is difficult to keep better unity in the dynamic performance and control precision, it puts forward a improved quasi-sliding mode variable structure control algorithm based on repetitive prediction control in HAPFSIC. For the control reference signal is a cycle volume, combined with rapid response of sliding mode variable structure control algorithm and the advantages of a good real-time non-steady-state error of repeated prediction control algorithm, it imports the control volume of repetitive prediction control algorithm as the equivalent control of improved discrete quasi-sliding mode variable structure controller, which makes it has three change state of switching on both sides as well as the within band. The simulation shows that: this new type of compound control method that overcomes the sliding mode variable structure control’s discrepancy regulation, a larger burr of current switch, and also avoids the shortcomings of repeated control’s longer time to reach steady-state, achieves organic combination of two control methods.