To address the issues of AC current sensor faults in grid-connected converters and unobservable regions in model predictive fault-tolerant control and high total harmonic distortion (THD) in the grid current, a model prediction fault-tolerant control strategy based on DC bus current reconstruction is proposed. First, according to the system structure of the grid-connected converter, the current prediction model is established. Then, the relationship between DC bus current and phase current under different voltage vectors is derived. The reconstruction principle of the three-phase current is analyzed, and the unobservable region of model predictive control during grid current sampling is clarified. Considering the relationship between the voltage vector action time and the minimum sampling time, virtual voltage vector set which can eliminate the unobservable region is designed and the fault-tolerant model predictive control strategy for grid-connected converters is proposed. The optimal vector is selected from the virtual vector set to achieve AC current sensor fault-tolerant model predictive control and reduce the total harmonic distortion of the grid current. Finally, experimental results verify the effectiveness of the proposed control strategy.