There are some unmeasurable areas in the fault-tolerant control for an AC current sensor fault in a virtual synchronous generator (VSG). This fact affects the fault-tolerant operation of VSG. To overcome this, a fault-tolerant model predictive control (MPC) strategy based on current reconstruction is proposed to eliminate unmeasurable areas and realize current reconstruction in whole areas. First, this strategy analyzes the corresponding phase current of measured DC current under different switching states, and designs the fault criterion of the AC current sensor. Second, the causes of unmeasurable areas are analyzed. They are divided into two kinds according to the insufficient number of measurable phase currents and vector durations that are too short. To eliminate the unmeasurable areas caused by the former, virtual vectors that can measure two-phase currents are designed, and three-phase currents can be reconstructed by DC current. To eliminate the latter, the output current prediction model of a VSG with an LCL filter is built, and three-phase currents can be reconstructed by DC current and the predictive currents of single voltage vectors. Finally, the optimal vector is selected from virtual vectors and single voltage vectors by the fault-tolerant MPC strategy, and the current reconstruction in whole areas and the fault-tolerant operation of a VSG are realized. The experiments verify the effectiveness of the proposed method. This shows that the proposed method improves the reliability and fault-tolerant ability of VSG.