As key component for the flexible dc distributed power system, the dual active bridge (DAB)-converter-based solid-state transformer (SST) with high efficiency for a wide operating range is essential. However, with the traditional phase-shift control, high backflow power and current stress will significantly affect the conversion efficiency. In this paper, the backflow power characteristics in both sides of DAB-based SST converters are comprehensively analyzed. On this basis, complete transmission power, backflow power, and peak current mathematical models are established. Then, a minimum-backflow-power-based extended-phase-shift control strategy is proposed with the determination of optimal phase-shift pairs by using the Karush–Kuhn–Tucker function for various scenarios. The backflow power and current stress curves with different algorithms are compared. It shows the proposed control can improve the output power regulation flexibility, minimize the backflow power, and improve the efficiency in wide operating range. Finally, a DAB-based SST prototype was developed and the experimental results verified the effectiveness of the proposed control strategy.