The size-dependence on the electronic and transport properties of the molecular devices of the edge-modified graphene nanoribbon (GNR) slices is investigated using density-functional theory and Green's function theory. Two edge-modifying functional group pairs are considered. Energy gap is found in all the GNR slices. The gap shows an exponential decrease with increasing the slice size of two vertical orientations in the two edge terminated cases, respectively. The tunneling probability and the number of conducting channel decreases with increasing the GNR-slices size in the junctions. The results indicate that the acceptor-donor pair edge modulation can improve the quantum conductance and decrease the finite-size effect on the transmission capability of the GNR slice-based molecular devices.