Modular multilevel converter (MMC) is especially appropriate in high-voltage constant-frequency systems due to its modularity and scalability. But, so far MMC has not been widely used in motor drives applications. Since the capacitor voltage fluctuation is proportional to the output current amplitude and inversely proportional to the output frequency under constant torque load, at the low-speed, the excessive sub-module (SM) capacitor voltage fluctuation is one of the major obstacles for MMC applied in motor drives. To suppress the SM capacitor voltage fluctuation, an effective solution is to inject a high frequency zero sequence voltage to the three-phase output voltages of MMC and control the circulating current per phase reasonably. However, the introduced high frequency and high amplitude common voltage at the motor side is harmful. In this paper, a hybrid MMC with cascaded full-bridge SMs (HMMC-CFB) topology is used in the medium-voltage motor drives. The high frequency and high amplitude common mode voltage is absorbed by the cascaded full-bridge SMs. Besides, the capacitor voltage fluctuations of each arm and the cascaded full-bridge SMs is easily limited within a reasonable range. Finally, the state space model of HMMC-CFB system is established and a stable state-error feedback control law is given. By the passive theory, the necessary and sufficient condition for the globally uniformly asymptotical stability of the HMMC-CFB closed-loop system is deduced. Simulation results confirm the superiority of this novel topology and the validity of the proposed control strategy.