General relativistic corrections to the expansion rate of the universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed cosmic acceleration. In this talk, we propose a new scheme that enables us to use N-body simulations to make a realistic estimate of the magnitude of these corrections for general inhomogeneities in (3+1) spacetime. We then quantitatively calculate the volume averaged modified expansion rate using the N-body simulation code Gadget_2 and compare it with the expansion rate in a standard FRW cosmology. We will also discuss its possible impacts on the cosmological observables.