Model predictive control (MPC) is widely used in modular multilevel converter (MMC) control because of its strong robustness, fast dynamic response, and strong stability. Traditional MPC must traverse several switch combinations to accurately regulate the output current and circulating current of the MMC. Therefore, as the number of sub-module (SM) grows, the controller's computational complexity grows. This paper proposes a compensatory model predictive current control (CMPCC) for inner loop current control. It immediately estimates the number of SMs required by the bridge arm without scrolling optimization, reducing the amount of calculation of the system and improving the output current and circulating current tracking accuracy to the references. The objective function is established based on the system output current and internal circulation current by developing the discretization mathematical model of MMC. On the basis of minimizing the optimization scope, the compensation prediction is achieved through the volt-second balance, to achieve effective current control. Subsequently, an uneven bucket sorting algorithm is proposed to drastically eliminate the unnecessary sorting process. Finally, both a MATLAB/Simulink model and an experimental platform of MMC are built. To verify the practicality of the proposed control strategy, simulation and hardware experiments are provided.