We investigate the low-threshold optical bistability of transmitted beams at the terahertz range based on the photonic crystal Fabry-Perot cavity with graphene. Graphene with strong nonlinear conductivity is placed in the middle of the Fabry-Perot cavity and the resonance of the cavity plays a positive role in promoting the low-threshold optical bistability. The optical bistability curve is closely related to the incident angle of light, the parameters of graphene, and the structural parameters of the Fabry-Perot cavity. Through parameter optimization, optical bistability with threshold of 105 V/m can be obtained, which has reached or is close to the range of the weak field.