Light modulation has been recognized as one of the most fundamental operations in photonics. In this paper, we theoretically designed a Bloch surface wave assisted modulator for the active modulation of graphene electro-absorption. Simulations show that the strong localized electrical field generated by Bloch surface waves can significantly enhance the graphene electro-absorption up to 99.64%. Then by gate-tuning the graphene Fermi energy to transform graphene between a lossy and a lossless material, electrically switched absorption of graphene with maximum modulation depth of 97.91% can be achieved. Meanwhile, by further adjusting the incident angle to tune the resonant wavelength of Bloch surface waves, the center wavelength of the modulator can be actively controlled. This allows us to realize the active modulation of graphene electro-absorption within a wide near-infrared region, including the commercially important telecommunication wavelength of 1550 nm, indicating the excellent performance of the designed modulator via such mechanism. Such Bloch surface waves assisted wavelength-tunable graphene electro-absorption modulation strategy opens up a new avenue to design graphene-based selective multichannel modulators, which is unavailable in previous reported strategies that can be only realized by passively changing the structural parameters.