Molecular spintronics has attracted much attention because of many novel functionalities at the single molecule level over the past decades.Recently,much research has focused on organic molecules containing transition metals in the field of molecular spintronics,which possesses desired spin-dependent transport properties for spintronic device applications. In this paper,based on non-equilibrium Green's function formalism combined with the first-principles density functional theory,the spin-dependent transport properties of an organic Co-Salophen molecule sandwiched between two zigzag graphene nanoribbon (ZGNR) electrodes are investigated.By applying an external magnetic field,the spin directions of the left and right ZGNR electrodes may be switched to two different configurations:the parallel (P) and antiparallel (AP) spin configurations.It is found that for the P spin configuration,the spin-up current is significantly larger than the spin-down one which is nearly zero in a bias range from -1.0 V to 1.0 V,exhibiting a nearly perfect spin filtering effect (up to 100%).Moreover,the spin-up current shows negative differential resistance behavior at 0.3 V.For the AP spin configuration,the spin-down current is much larger than the spin-up one at the positive bias.On the contrary,the spinup current is much larger than the spin-down one at the positive bias.Therefore,the device exhibits bipolar spin filtering effect.It is also found that the spin-up current at the negative bias is much larger than that at the corresponding positive bias,while the spin-down current at the negative bias is much smaller than that at the corresponding positive bias,which shows the outstanding spin rectifying effect.Besides,a significant giant magnetoresistance effect is also obtained in the device when the spin directions of the left and right ZGNR electrodes switch between P and AP spin configurations. The spin transport properties of the device under P and AP spin configurations are attributed to the different orbital symmetries of spin subbands (* and ) of the electrodes and the spatial distribution of molecular orbitals within the bias window.By analyzing the spin-polarization transmission spectrum,the local density of states,the band structures and symmetries of the ZGNR electrodes and the projected self-consistent Hamiltonian states of molecular orbitals,the internal mechanism for multiple functional characteristics of the device is explained in detail.Our results indicate the Co-Salophen molecule can be a promising candidate for future applications in molecular spintronics device,and also provide a theoretical reference for designing the next-generation molecular nano-devices.