Modular multilevel converters (MMCs) have gained widespread adoption in high-voltage direct current (HVDC) transmission due to their high voltage levels, low harmonic content, and high scalability. However, conventional control methods such as finite control set model predictive control (FCS-MPC) suffer from a heavy computational burden and sensitivity to system parameter variations, limiting the performance of MMCs. This paper proposes a data-driven approach based on model-free adaptive control with an event-triggered mechanism that demonstrates superior robustness against parameter mismatches and enhanced dynamic performance in response to sudden output changes. Moreover, the introduction of the event-triggered mechanism effectively reduces redundant operations, decreasing the computational burden and switching losses. Finally, the proposed strategy is validated through a MATLAB/Simulink simulation model.