The magnetic state of a spintronic device is usually controlled by magnetic contacts or a transverse electric field generated by side gates. In this work, we consider a graphene nanojunction in the presence of a bias voltage that leads to magnetic phase transitions in the system. Combining the non-equilibrium Green’s function with the Hubbard model, our self consistent calculation reveals that an increasing bias voltage induces consecutive transitions among antiferromagnetic and ferromagnetic states. It is further shown that the graphene nanojunction is turned off in the antiferromagnetic state when the bias voltage is low and can then be switched on to the ferromagnetic state by a high bias voltage. We therefore demonstrate that the magnetic state of the graphene system can be controlled by the bias voltage without resorting to any transverse gates.