Graphene is an attractive material for optoelectronics and photodetection applications because it offers a broad spectral bandwidth and fast response times. However, weak light absorption and the absence of a gain mechanism that can generate multiple charge carriers from one incident photon have limited the responsivity of graphene-based photodetectors to ∼10(-2) A W(-1). Here, we demonstrate a gain of ∼10(8) electrons per photon and a responsivity of ∼10(7) A W(-1) in a hybrid photodetector that consists of monolayer or bilayer graphene covered with a thin film of colloidal quantum dots. Strong and tunable light absorption in the quantum-dot layer creates electric charges that are transferred to the graphene, where they recirculate many times due to the high charge mobility of graphene and long trapped-charge lifetimes in the quantum-dot layer. The device, with a specific detectivity of 7 × 10(13) Jones, benefits from gate-tunable sensitivity and speed, spectral selectivity from the short-wavelength infrared to the visible, and compatibility with current circuit technologies.