We study the holographic dark energy on the subject of Hoˇrava-Lifshitz gravity with a time dependent gravitational constant G(t), in the non-flat space-time. We obtain the differential equation that specify the evolution of the dark energy density parameter based on varying gravitational constant.We find out a relation for the state parameter of the dark energy equation of state to low red-shifts which containing varying G corrections in the non-flat space-time.
