The cascaded H-bridge static synchronous compensator (STATCOM) has been widely employed in medium- and high-voltage reactive power compensation applications due to its high modularity, fast response speed, and direct grid connection capability. However, the DC-link voltage exhibits an inherent double-frequency ripple, which poses a serious challenge to power quality. Therefore, numerous Active Power Decoupling (APD) techniques have been proposed. However, existing schemes still exhibit certain limitations: independent APD topologies are associated with higher costs, whereas single bridge-arm multiplexed APD topologies are confronted with issues such as elevated DC-side voltage and increased current stress on the multiplexed arm. Consequently, comprehensive optimization is difficult to achieve in terms of the number of power devices, decoupling accuracy, level of capacitor multiplexing, and device stress. To address the above issues, this paper proposes a DC split capacitor (DC-SC)-based dual bridge-arm multiplexed cascaded H-bridge STATCOM with active power decoupling capability, along with its corresponding control method. By constructing a fundamental-frequency common-mode voltage on the decoupling capacitor, this method effectively suppresses the double-frequency ripple in the DC-side voltage and reduces the current stress on the switching devices. The simulation and experimental results have verified the correctness and effectiveness of the proposed topological structure and control method.