A theoretical study of zigzag graphene nanoribbons (ZGNRs) with an epoxy-pair chain (ZGO) is performed. The electronic transport properties are mainly evaluated by non-equilibrium Green's functions using the TRANSIESTA package. The results indicate that the graphene oxide can have a negative differential resistance (NDR) phenomenon, supported by bias-dependent transmission curves of different spin orientations. Applying non-zero bias voltages makes the density of states (DOS) of the right electrodes shift down. Due to an energy gap between the LUMO and LUMO+1 in ZGOs, with a certain bias, the conduction band of the right electrode cannot match the LUMO of the scattering region, then NDR occurs. With a larger bias, NDR ends when the second conduction band of the right electrode's DOS covers the LUMO of the scattering region. Since most of proposed ZGO systems possess such a gap between the LUMO and LUMO+1, NDR can be widely observed and this discovery may provide great potential applications in NDR-based nanoelectronics by using modified graphene materials.