The Super-Kamiokande-Gd (SK-Gd) experiment is one of the largest neutrino experiments sensitive to an energy region from a few MeV to TeV. It has a Gd-loaded water Cherenkov detector and the capability to identify delayed neutron signals associated with prompt interaction. We aim to observe Diffuse Supernova Neutrino Background which is collective neutrino flux from all supernovae in the universe, and search for electron anti-neutrinos via an inverse beta decay channel, $\bar{\nu}_e + p \rightarrow e^{+} + n$. In addition, there is a $\bar{\nu}_e$ flux coming from reactors, which has not been observed yet in the SK, around the peak energy of DSNB flux, $\sim 5$ MeV. The latest result of the SK-Gd is conducted with an energy threshold of 7.5 MeV in kinetic energy. This energy threshold is determined by the trigger system. To extend the lower energy region, we are developing a new analysis method of $\bar{\nu}_e$. We expect a better understanding of background events in the DSNB search and the first reactor signal in the SK. I describe the new method and the result of a feasibility study using
muon spallation events in this paper.