Modular multilevel converter(MMC) has drawn great attention in variable-speed machine drives. However, a challenge exists that the voltage ripple of sub-module capacitors in MMC would be very large at low motor speed. In this paper, a novel back-to-back(BTB) MMC system is introduced which can effectively limit the capacitor voltage ripple. The grid-side MMC is a hybrid structure which uses full-bridge sub-modules in the upper arm whereas half-bridge sub-modules in the lower arm. The DC-link current is controlled to be constant thus the motor-side MMC with half-bridge sub-modules can reduce its DC-link voltage at low frequencies so as to absorb less energy variation and limit the capacitor voltage ripple. The operating principle of this hybrid BTB MMC system and the corresponding control strategies are discussed. The effectiveness has been validated by simulation and experimental results.