With the miniaturization of molecular devices, high-performance nano devices can be fabricated by controlling the spin states of electrons. Because of their advantages such as low energy consumption, easy integration and long decoherence time, more and more attention has been paid to them. So far, the spin filtration efficiency of molecular device with graphene electrode is not very stable, which will decrease with the increase of voltage, and thus affecting its applications. Therefore, how to enhance the spin filtration efficiency of molecular device with graphene electrode becomes a scientific research problem. Using the first principle calculations based on density functional theory combined with non-equilibrium Green’s function, the physical mechanism of regulating the spin polarization transport properties of single anthracene molecule device with graphene nanoribon as electrode is investigated by molecular oxygen adsorption. In order to explore the effect of the change of the connection mode between single anthracene molecule and zigzag graphene nanoribbon electrode on the spin transport properties of the device, we establish two models. The first model is the model M1, which is the single anthracene molecule longitudinal connection, and the second model is the model M2, which is the single anthracene molecule lateral connection. The adsorption model of single oxygen molecule is denoted by M1O and M2O respectively. The results show that when none of oxygen molecules is adsorbed, the spin filtering effect of single anthracene molecule connecting graphene nanoribbons laterally (M2) is better than that of single anthracene molecule connecting graphene nanoribbons longitudinally (M1). After oxygen molecules are adsorbed on single anthracene molecule, the enhanced localized degree of transport eigenstate will make the spin current of the two kinds of devices decrease by nearly two orders of magnitude. However, molecular oxygen adsorption significantly improves the spin filtering efficiency of the device and enhances the application performance of the device. The maximal spin filtering efficiency of single anthracene molecule connecting graphene nanoribbons longitudinal (M1O) can be increased from 72% to 80%. More importantly, the device with single anthracene molecule connecting graphene nanoribbons laterally (M2) maintains nearly 100% spin filtering efficiency in a bias range from –0.5 V to +0.5 V. These results provide more theoretical guidance for practically fabricating spin molecular devices and regulating their spin transport properties.