This paper proposes the model predictive control with the space vector modulation (MPC-SVM) method for the current control of the voltage source inverter (VSI). Unlike the conventional MPC method using the limited number of voltage vectors by switching states, the various voltage vectors can be taken into account to find the optimized voltage vector in the proposed method. The various voltage vectors are obtained by subdividing existing voltage vectors more. Among them, some voltage vectors, which are determined by the reference voltage angle (Oref) and magnitude dVrefi), are used to calculate the cost function to mitigate high computational load during the prediction. The various voltage vectors and SVM reduce the current ripples in the output AC side of the inverter compared to the conventional MPC method. The effectiveness and performance of the proposed method are verified by PSIM simulation and experimental results with a three-phase two-level voltage source grid-connected inverter.