Under light load conditions, the phase-shifted full-bridge (PSFB) converter often has difficulty in realizing the zero-voltage switching (ZVS) of the lagging-leg by relying on the energy of its resonant inductor; however, for the series-parallel PSFB converter applied in high-power applications, the lagging-leg still has the problem of difficult realization of ZVS. Based on this, the paper analyzes the reasons why the series-parallel PSFB converter has difficulty in achieving ZVS for the lagging-leg under light and heavy loads. Under interleaved control, the ZVS of the lagging-leg over the full load range is realized by adding an auxiliary LC branch at the midpoint of the lagging-leg of both submodules. Based on the double-bridge input-parallel-output-series (IPOS) PSFB converter, analyzing the working principle of the circuit after adding the auxiliary LC branch and extending it to the series-parallel PSFB converter. The design requirements of the LC auxiliary branch of the dual-bridge series-parallel PSFB converter are given and the effects of the LC auxiliary branch on the module operating state and device stress are analyzed. On this basis, an extension is carried out to give the working principle and design method of the auxiliary LC branch of the N-bridge series-parallel PSFB converter. Finally, a 100 kW Matlab/Simulink simulation model verifies the superior performance of the proposed LC auxiliary branch to realize the lagging-leg ZVS of the series-parallel PSFB converter under light and heavy loads and achieves a 1.09% peak efficiency improvement at rated load.