The modular multilevel matrix converter ((MC)-C-3) is an ac-to-ac converter topology suitable for the control of high-power variable-speed drives. The control of this converter is complex, particularly when the two ac system frequencies are similar or identical because large voltage oscillations can be produced in the floating capacitors within the (MC)-C-3. This paper proposes a new vector control system based on nested controllers to regulate the (MC)-C-3 over the full range of frequencies. The proposed control scheme is especially useful to mitigate or eliminate the oscillations that arise when the frequencies are similar. An extensive discussion of the model and control of the (MC)-C-3 is presented in this work. The effectiveness of the proposed vector control system is demonstrated through simulation studies and experimental validation tests conducted with a 27-cell-5kW (MC)-C-3 prototype.