Graphene is potentially attractive for spintronics due to its weak intrinsic spin–orbit effect leading to a long spin relaxation length. This study examines molecular couplings on a planar graphene sheet, where one molecule is attached to the graphene sheet connected to ferromagnetic leads. The effects of a strong magnetic field, gate voltage, and time-dependent bias voltage on spin and charge tunneling currents are investigated. It is indicated that the studied model system could be controlled by applying a gate voltage and a time-dependent bias voltage. Regarding the interaction between graphene, magnetic molecule, and magnetic field, it is observed that the mutual interaction coefficients between them have the most considerable effect on the transport current. Applying the magnetic field shows that the response time of the current is very short, and the current is not zero in the steady state. In this situation, the current passes through the system continuously.