The modular multilevel converter (MMC) is widely utilized in high-voltage direct current (HVDC) transmission systems due to its modular design, scalability, and fault tolerance. Although conventional model predictive control (MPC) offers the advantages of a fast dynamic response and simple implementation, its application is limited by high computational burden and insufficient circulating current suppression. To address these issues, a hybrid model predictive control (H-MPC) strategy is proposed, which combines an improved indirect MPC with a fractional-order quasi-proportional-integral-resonant (FO-QPIλR) controller. The improved indirect MPC optimizes control objectives and simplifies the rolling optimization process, significantly reducing the computational burden while avoiding the complexity of weighting factor tuning in conventional MPC, thereby achieving fast current tracking and submodule capacitor voltage balancing. Meanwhile, the FO-QPIλR controller exhibits better dynamic performance and robustness than a traditional PI controller, effectively suppressing the circulating current without the need for decoupling. To validate the effectiveness of the proposed strategy, a comparison with the conventional indirect MPC strategy was conducted. Simulation results show that the circulating current amplitude is reduced by 80% and the submodule capacitor voltage fluctuation is decreased by 9%; experimental results further demonstrate a 53% reduction in circulating current amplitude and a 10% reduction in submodule capacitor voltage fluctuation. The simulation and experimental results indicate that the proposed hybrid control strategy, while maintaining the fast dynamic response and high-quality output current of MPC, significantly suppresses circulating current harmonics and enhances the submodule capacitor voltage balancing capability, thus verifying the effectiveness and superiority of the strategy.