Within the nearest-neighbor tight-binding theory, the low-energy conductance of graphene nanoribbons (GNRs) has been numerically calculated by using the Green's function method. The effects of the coupling between the GNRs and the electrodes on conductance oscillations of GNRs have been investigated. It is shown that the conductance oscillations appear at strong coupling. It is interesting to find that, on the first conductance step, all GNRs have only one quasiperiodic conductance oscillation; on the second conductance step, the zigzag edge GNRs and semiconducting armchair edge GNRs have two quasiperiodic conductance oscillations, i.e., a rapid conductance oscillation over a slow fluctuation background, while the metallic armchair edge GNRs have only one conductance oscillation. The mechanism underlying the origin of the conductance oscillations has been revealed.