The single-stage half-bridge matrix (SBM) converter has attracted considerable attention owing to its high power density and efficiency. However, substantial variations in input AC voltage and the influence of bridge arm capacitors on inductor current fluctuations pose challenges for existing modulation strategies to ensure efficient operation across the entire operating range. Therefore, this paper proposes a high-efficiency, multi-degree-of-freedom (DOF) modulation strategy for the SBM converter. This strategy minimizes the root mean square current and guarantees zero-voltage switching for all power switches, thereby optimizing the converter's efficiency over a broad input voltage range while taking into consideration the impact of bridge arm capacitors. Firstly, a time-domain analysis of the three-DOF modulation strategy is conducted. Subsequently, optimization is achieved by reducing the peak-to-peak current, and its steady-state characteristics are compared with those of recent related studies. Finally, an experimental prototype is constructed to validate the effectiveness of the proposed modulation strategy. The results indicate that the proposed strategy can improve efficiency by approximately 6.61% compared to recent optimization approaches.