This paper presents a modular multilevel cascade converter based on triple-star bridge-cells (MMCC-TSBC) with a focus on its decoupled control. The TSBC is one of the direct ac-to-ac power converters having the capability of bidirectional power flow with three-phase sinusoidal input (supply-side) and output (motor-side) currents. Therefore, it is suitable for a medium-voltage motor drive requiring regenerative braking. This paper has an intensive discussion on control strategy for the TSBC, which includes current control, capacitor-voltage-balancing control, and fluctuation-mitigating control for low-speed operation. This control strategy succeeds in achieving decoupling among supply (input) currents, motor (output) currents, and circulating currents, using the αβ0 coordinate transformation. The validity and effectiveness of the control strategy are confirmed by theoretical analysis and computer simulation.