This paper presents a control scheme for the Modular Multilevel Converter (MMC) to drive a variable- speed AC machine, especially focusing on improving dynamic performance. Theoretically, the energy balance in the MMC cell capacitors is prone to be unstable at start-up and at low frequency operations. Additionally, the MMC topology essentially requires advanced control strategies to balance energy and suppress the voltage pulsation of each cell capacitor. This paper proposes a control strategy for the robust dynamic response of MMC even at zero output frequency employing leg offset voltage injection. The leg offset voltage for balancing the arm energy is produced by direct calculation without the circulating current control loop controller. Thanks to the highly dynamic leg offset voltage from direct calculation and not conventional circulating current controller, the dynamic performance of the MMC at low speeds has conspicuously improved. The AC machine has been driven from standstill to rated speed without excessive cell capacitor voltage ripples utilizing this proposed strategy. The simulation and experimental results verify that stable operation is guaranteed down to less than 2 % of the rated speed under 40% step load torque disturbance.