The over-modulation capability of the hybrid modular multilevel converter (MMC), mixed by half-bridge and full-bridge submodules (SMs), has acquired widespread attention recently, which can significantly increase the design freedom of the hybrid MMC. When the hybrid MMC is applied in the medium-voltage occasions, an improved carrier phase shift pulsewidth modulation (CPS-PWM) approach is put forward in this article for its over-modulation operation under the nominal and variable dc conditions. It is featured with high flexibility, adjustability, and simple implementation. A new standard voltage is introduced to normalize the modulation wave, by which there is always a sufficient margin between the peaks of the normalized modulation wave and carrier waves under any modulation indexes. Also, it can perform well when the nominal dc voltage of the hybrid MMC is not the integer multiple of SM voltage. Moreover, the carrier wave arrangements are decoupled with the number of SMs, dc voltage, and ac voltage, so the variable dc operation of the hybrid MMC can be achieved without rearranging the carrier waves. Finally, the simulations and experiments are carried out to confirm the effectiveness of the proposed CPS-PWM approach for over-modulation operations under the steady-state and variable dc conditions.