Due to the large-scale renewable energy connected to the power grid by power electronic converters, the inertia and stability of the power grid is declining. In order to improve the inertia and support the grid recovery, the three-phase converter works as a virtual synchronous generator (VSG) to respond to the frequency and voltage changes of the power grid. This paper proposes a model predictive control for the virtual synchronous generator (MPC-VSG) strategy, which can automatically control the converter output power with the grid frequency and voltage changes. Further consideration of fault-tolerant ability and reliability, the method based on improved voltage vector selection, and reconstructed current is used for MPC-VSG to ensure continuous operation for three-phase converters that have current-sensor faults, and improve the reconstruction precision. The proposed method can respond to the frequency and voltage changes of the power grid and has fault-tolerant ability, which is easy to realize without pulse width modulation (PWM) and a proportional-integral (PI) controller. The effectiveness of the proposed control strategy is verified by experiment.