In this paper, dayside magnetopause energy transport (energy transport across the separatrix surface to the magnetopause boundary layer and energy transport inside the magnetopause boundary layer) and its dependence on the magnetopause dynamic evolution under purely southward interplanetary magnetic field (IMF) conditions are studied via a 3-D global hybrid simulation. By investigating the energy transport across the separatrix surface, current layer surface, and magnetopause surface, we find that the energy transport from the magnetosheath to the magnetopause boundary layer is mainly in the form of electromagnetic energy, while the energy transport directly across the magnetopause surface to the magnetosphere is mainly in the form of plasma energy. The energy transport across the magnetopause surface exhibits temporal variability, driven by the dynamic evolution of reconnection and flux rope. During the development of multiple X-lines reconnection and flux rope, a substantial portion of solar wind energy does not directly penetrate the dayside magnetopause to the magnetosphere. Instead, it is transported with the reconnection outflow and flux rope from low latitude to high latitude, and with the drifting flow from the subsolar region to the tail magnetopause within the magnetopause current layer. These results significantly improve our understanding of solar wind-magnetosphere coupling at the dayside magnetopause.