In order to reduce the inductor current rms value of the dual active bridge (DAB) converter and extend the soft switching range over a wide voltage range, this article proposes an optimal dual-side asymmetric modulation (ODSAM) strategy which significantly improves the efficiency, especially at light load. First, the principle of asymmetric duty modulation (ADM) is introduced, the operating modes of dual-sided asymmetric modulation (DSAM) are established, and two suitable operating modes are selected to improve efficiency according to the principle of minimum reactive power. Second, the equivalent circuit model and steady-state mathematical model are further analyzed. Third, combined with the soft-switching constraints, the peak-to-peak value of the inductor current is selected as the optimization objective, global optimal solution using the Lagrange multiplier method (LMM) is obtained. Then, the control strategy of the ODSAM based on the global optimal solution is proposed. Finally, an experimental platform of a DAB converter with a rated power of 360 W is built, and the effectiveness of the proposed ODSAM strategy is verified.