Modular Multilevel Converter (MMC) is widely used in applications such as High Voltage Direct Current (HVDC) transmission, AC/DC power conversion centers, and large-scale power quality management in electrical grids due to its highly modular structure, strong redundancy and low harmonic content in AC output. The application of the traditional deadbeat predictive current control to MMC enhances the fast tracking ability of the output current, but it still has the problems of low output current accuracy and high dependence on bridge arm inductor. Based on this, this paper proposes an improved two-beat deadbeat synchronous predictive current control based on Newton interpolation method. By improving the two-beat deadbeat synchronous predictive current control strategy, the accuracy of the output current can be further improved and its fast tracking ability can be enhanced. Newton interpolation is introduced to improve the accuracy of the output current while reducing the dependence on the bridge arm inductor. The results show that the control strategy proposed in this paper reduces the output current THD by 2.88% compared with the two-beat deadbeat predictive current control, thus improving the accuracy; the bridge arm inductor value is reduced by 1.28%, thus reducing the dependence; and under the transient environment, the output current can be tracked to its predicted reference value 843 μs in advance, which enhances the fast tracking capability.