A control strategy based on finite control set model predictive control（FCS-MPC）is introduced as its current control strategy in order to improve both steady and dynamic compensation feature of midpoint active power filter（APF）of three-phase four-wire capacitor. Firstly

the discrete prediction model of system is established and derived at three-dimensional coordinate system to solve the problem of threephase coupling and unbalanced current. Then

all the prediction currents are calculated in accordance with the pre-diction model and the optimal switching state is found as output by way of traversal method

with purpose of fast tracking the command current and the control is very simple without modulation link. At the same time

double loop PI control is adopted to achieve the stability and balance of capacitor voltage at DC side. Finally

the feasibility and effectiveness of the strategy in APF system control is verified through the simulation comparison with compound control method.