Current stresses in dual-active-bridge (DAB) converters increase rapidly in the event of voltage mismatch between the two sides. Excessive current stress not only complicates the selection of switching devices, but also reduces the efficiency and operational safety of the DAB. To address this issue, a global minimum current stress control strategy based on dual phase-shift (DPS) control is proposed. First, the feasible region of the phase-shift pairs under DPS control is analyzed. Based on the analytical expressions of transmission power and current stress in each region, an optimization model for minimizing DAB current stress over the full power range is established. For the multi-region and non-convex current stress optimization problem, the global optimal solution region is first identified by analyzing the results obtained from a genetic algorithm. Then, using the KKT conditions, an analytical expression for the global optimal solution is derived, leading to the proposed DPS-based minimum current stress control strategy for DAB converters. Subsequently, the soft-switching characteristics of the DAB under the optimized control are analyzed. Finally, the correctness and effectiveness of the theoretical analysis and the proposed control strategy are verified through experiments.