Graphene has been widely used in silicon-based optical modulators for its ultra-broadband light absorption and ultrafast optoelectronic response. By incorporating graphene and slow-light silicon photonic crystal waveguide (PhCW), here we propose and experimentally demonstrate a unique double-layer graphene electro-absorption modulator in telecommunication applications. The modulator exhibits a modulation depth of 0.5 dB/μm with a bandwidth of 13.6 GHz, while graphene coverage length is only 1.2 μm in simulations. We also fabricated the graphene modulator on silicon platform, and the device achieved a modulation bandwidth at 12 GHz. The proposed graphene-PhCW modulator may have potentials in the applications of on-chip interconnections.