This paper proposes a deadbeat finite set model predictive current control based on discrete space vector modulation (DSVM) in order to achieve robust characteristics from the grid impedance variation while guaranteeing high performance of output current waveforms and a fixed switching frequency. The proposed DSVM strategy enables to obtain a large number of virtual voltage vectors without complex initialization process or lookup table, which are the drawbacks of the conventional DSVM strategies. A deadbeat technique was adopted to minimize the number of candidate voltage vectors considered in the cost function in order to avoid the high computational burden caused by considering all voltage vectors. The simulation and experimental results were presented to verify the effectiveness and performance of the proposed method using a two-level grid-connected voltage source inverter.