The modular multilevel matrix converter (M3C) has shown promising application prospects in medium-to high-voltage high-power scenarios such as large-scale motor drives and wind power integration, owing to its modular structure, high reliability and superior power quality. However, in traditional cascaded control strategies, the outer-loop proportional-integral（PI） controller exhibits limited response speed, while the inner-loop PI controller lacks sufficient robustness against system parameter perturbations and external disturbances, constraining the dynamic performance of the M3C under complex operating conditions. To address these issues, this paper proposes a cascaded control strategy for the M3C based on an inner-loop robust backstepping sliding mode control. This strategy retains the outer-loop PI control to ensure steady-state error-free tracking of power commands, with the core innovation lying in the inner-loop adoption of robust backstepping sliding mode control. By recursively designing the control law via the backstepping approach and incorporating a sliding mode term, it effectively integrates precise linearization with strong disturbance rejection capabilities. The global asymptotic stability of the closed-loop system is rigorously demonstrated based on Lyapunov stability theory. MATLAB/Simulink simulation results indicate that, compared to the conventional dual-PI cascaded control, the proposed strategy offers faster dynamic response, reduced overshoot and enhanced parametric robustness under transient conditions such as load sudden changes and grid voltage asymmetry, significantly improving the system′s control performance.