Compared with other topologies, the modular multilevel converter (MMC) has the advantages of higher scalability and lower harmonic distortion. When carrier-based pulse-width modulation approaches are used for the MMC, the number of carriers increases for more sub-modules, and the complexity of the control and the memory required increases as a result. In addition, the synchronization of several carriers is another issue. Due to the unique constructional characteristics of the MMC, circulating currents will be generated internally, causing distortions in the arm currents and, thus, unnecessary converter losses. In this paper, an improved 2N+1 pulse-width modulation approach with low control complexity and a circulating current suppression strategy are proposed. Firstly, the conventional carrier phase-shifted 2N+1 pulse-width modulation approach is improved so that the number of carrier signals adopted in each arm is always two. Secondly, the redundant switching states are used to suppress the circulating current. Finally, the effectiveness of the proposed strategy is verified experimentally. The results show that the proposed method reduces the control complexity while retaining the output performance. Meanwhile, the circulating current can be suppressed.