The complete mathematical model is established for three-phase four-wire active power filters（APF）. A novel deadbeat control scheme based on repetitive harmonic predictor is proposed to improve the dynamic performance of three-phase four-wire APFs. The principle of the novel deadbeat control scheme， the discrete time model of the control system and the working principle of the repetitive harmonic predictor are presented in detail.The sufficient condition for keeping the repetitive harmonic predictor stable is also discussed in the paper. The MATLAB/Simulink based simulation analysis of the APF control system shows that the dynamic response of the control system is effectively improved and the steady state accuracy is good enough by implementing the novel deadbeat control scheme.