The mathematical model of active power filter (APF) has important implications for the design of controller and the analysis of AC/DC energy transfer. On the basis of the mathematical model established for widely used parallel APF main circuit topology, a circuit control strategy of variable frequency hysteresis SVPWA is used. Three-phase three-wire APF model is analyzed and established in detail, and the design method of controller is given. The simulation verification confirms that the mathematical model of parallel APF established is correct, and the control strategy could be a very good reference.