The Input-serial-output-parallel (ISOP) dual-active-bridge (DAB) converter is an attractive solution to be used as a DC transformer (DCT) in the DC power distribution system. However, due to zerovoltage-switching (ZVS) limitation and large circulating current, the efficiency of the converter will be reduced. To improve the efficiency, an ISOP DAB converter based on a modulated coupled inductor, and a corresponding hybrid SPS control are proposed in this paper. With the hybrid SPS control strategy, the equivalent leakage inductance of modulated coupled inductor can be controllable. The large inductance is adopted at light load and the small inductance for the transformer is applied at heavy load to reduce circulating current and extend the ZVS range. By optimizing the root-mean-square (RMS) current of two operation modes of the converter, a control boundary of the hybrid SPS control can be obtained to modulate the coupled inductor. Meanwhile, the additional magnetizing inductance is utilized to achieve ZVS for all switches. The analysis based on the RMS current optimization and ZVS condition is given. Based on the conditions of the full load range ZVS and small RMS current, the parameters of the modulated coupled inductor, the turn ratio of the transformer, and magnetizing inductance are designed. Finally, a 250kHz, 800/400V, 2000W ISOP DAB prototype is built to verify the effectiveness of the proposed method. Meanwhile, a comparison experiment with the conventional individual leakage inductors solution is given, which shows performance improvements of the proposed solution.