The terahertz (THz) modulators, as an essential component of the THz system, have been developed by many efforts until now. However, the development of flexible THz modulators is hindered due to the lack of flexible THz modulating materials. Herein, for the first time to the best of our knowledge, we demonstrated the feasibility of flexible THz modulators based on the coplanar-gate field-effect transistor (FET) structure of ion-gel/graphene/polyethylene terephthalate. The THz transmittance through this THz graphene modulator can be well controlled with a modulation depth up to 22% by tuning the carrier concentration of graphene via electrical gating. Furthermore, because of the integration of high flexibilities of graphene, ion-gel, and polyethylene terephthalate (PET), the proposed THz graphene modulator shows superior flexible performance, where the modulation properties can be maintained almost unchanged, not only under bending deformations, but also before and after bending 1000 times. In addition, due to the unique structure of ion-gel/graphene/PET, the flexible THz graphene modulator has a low insertion loss (1.2 dB). Therefore, this Letter is expected to be beneficial for the potential applications, ranging from the traditional compact THz system to a new flexible THz technology.