The illumination of single-layer graphene (SLG) transistors with visible light causes a negative shift in their transfer curves, attributable to the desorption of oxygen. However, their hysteresis is not affected by illumination, which suggests that charge traps are not affected by the visible-light exposure. When SLG transistors are covered with a layer of photoactive polymer, the photodesorption-induced current change in the transistors becomes less significant than the effects caused by the surrounding photoactive polymer. These observations demonstrate that the photoelectrical response of SLG transistors is dominated by extrinsic mechanisms rather than by the direct photocurrent process. The results suggest a new strategy for achieving light detection. The large cross section of SLG films for receiving photons and the capability of tailoring photoelectrical properties on them is potentially useful for optoelectronic applications.