In this paper, we propose an optical bistable structure based on a single graphene layer sandwiched between two magnetooptical layers which are located between two photonic crystals. It is indicated that such structure shows optical bistability behaviors, in the near infrared range, which can be efficiently controlled with small external magnetic fields lower than 1.5 mT. Such weak external magnetic fields cannot affect the graphene layer and the dependence of bistability phenomenon on the magnetic field results from the presence of magnetooptical layers and their influences on the resonance frequency of the structure. Both switch-up and switch-down thresholds can be significantly adjusted by variation of the external magnetic field. Furthermore, the width of hysteresis loop enhances with increasing the magnetic field. To obtain a high tunability of bistability with external magnetic fields, the thickness of magnetooptical layers should be larger than a special value. It is also found that the increase of the Fermi energy level of graphene leads to the enhancement of both switch-up and switch-down thresholds as well as the width of the hysteresis loop. Finally, it is confirmed that optical bistability can be manipulated by changing the incident illumination angle.