Active manipulation of light in optical fibers has been extensively studied with great interest because of the structure simplicity, small footprint, low insertion loss and the compatibility with diverse fiber-optic systems. While graphene can be seen to exhibit a strong electro-optic effect originating from its gapless Dirac-fermionic band structure, there is no report on the electro-absorption properties of all-fiber graphene devices. Here a novel tunable graphene-based hollow optical fiber structure is designed with graphene coated on the inner wall of the fiber central core. Evanescent field of the guided mode propagating in the hollow optical fiber interacts with a monolayer or stacked multilayer graphene, which could modulate the intensity of the propagating mode via altering the chemical potential of the graphene by an external electric field. A full vector finite element method is adopted to analyse the influences of the chemical potential, the air-hole's radius and layers of graphene on the electro-optic modulation properties of the structure. Numerical simulation results show that by adjusting the chemical potential of graphene, the phase and on-off features of the fiber can be tuned correspondingly, as well as the position, magnitude and width of the loss peak and the sub-peak. However, the air-hole's radius and layers of graphene will only affect the loss variation, the magnitude and width of the loss peak and the sub-peak, but have no influence on the on-off point and the position of the loss peak and the sub-peak. In addition, the loss variation caused by N-layer graphene is N times that of the monolayer graphene. Since it is the dielectric constant of graphene that determines the effective refractive index and the loss of the fiber, the dielectric constant is only related to its chemical potential while independent of the air-hole's radius and the layers of graphene. Finally, an optimal electro-absorptive modulator based on the penta-layer graphene-coated hollow optical fiber is proposed for its advantage of ultra-compact footprint (5 mm 125 m), ultrawide optical bandwidth (580 nm), high extinction ratio (16 dB), high modulation bandwidth (64 MHz) and low insertion loss (1.23 dB), as well as a broad operational spectrum that ranges from 1180 to 1760 nm. Our results can provide theoretical references for the design and application of graphene-based tunable photonic fiber devices.