Direct detection of sub-MeV dark matter has emerged as the next frontier in dark matter search area due to the null detection signal in the higher mass regime. In this work, we propose two-dimensional bilayer stack of graphene to detect sub-MeV dark matter. Its voltage-tunable sub-eV electronic band gap makes it an excellent choice for the detector material of a light dark matter search. We compute the detector response and estimate the projected sensitivity to constrain sub-MeV dark matter-electron scattering and sub-eV dark matter absorption parameter spaces. We show that a bilayer graphene dark matter detector exhibit competitive sensitivity as other target materials, such as superconductor, but with a tunable energy gap. Moreover, the daily modulation in the dark matter scattering rate from the rotation of the Earth which may help us mitigate the backgrounds.