Integration of electronics and photonics for future applications requires an efficient conversion of electrical to optical signals. The excellent electronic and photonic properties of graphene make it a suitable material for integrated systems with extremely wide operational bandwidth. In this paper, we analyze the novel geometry of modulator based on the rib photonic waveguide configuration with a double-layer graphene placed between a slab and ridge. The theoretical analysis of graphene-based electro-absorption modulator was performed showing that a 3 dB modulation with ~ 600 nm-long waveguide is possible resulting in energy per bit below 1 fJ/bit. The optical bandwidth of such modulators exceeds 12 THz with an operation speed ranging from 160 GHz to 850 GHz and limited only by graphene resistance. The performances of modulators were evaluated based on the figure of merit defined as the ratio between extinction ratio and insertion losses where it was found to exceed 220.