In islanded mode, the output power of PV-storage DC microgrids is significantly affected by external environmental factors. To improve the system’s maximum power point tracking (MPPT) characteristics, a push-pull converter based independent photovoltaic power generation topology is adopted in this paper. To address the issues such as chattering and slow response in traditional sliding mode control (SMC) for MPPT, this paper proposes an improved super-twisting sliding mode control method based on a modified super-twisting reaching law. By leveraging the continuity of the sigmoid function in combination with the fast terminal sliding mode surface, the proposed method optimizes the super-twisting reaching law, reduces chattering, and improves response speed. Matlab/Simulink simulations are used to compare with other methods and verify the proposed control strategy. The results show that in the absence of external disturbances, the proposed method can achieve fast and accurate MPPT with minimum chattering. When irradiance or temperature varies, the system shows better dynamic response and enhanced disturbance rejection capability.