We report an improved photosensitivity in few-layer tin disulfide (SnS2) field-effect transistors (FETs) following doping with CdSe/ZnS core/shell quantum dots (QDs). The hybrid QD-SnS2 FET devices achieve more than 500% increase in the photocurrent response compared with the starting SnS2-only FET device and a spectral responsivity reaching over 650 A/W at 400 nm wavelength. The negligible electrical conductance in a control QD-only FET device suggests that the energy transfer between QDs and SnS2 is the main mechanism responsible for the sensitization effect, which is consistent with the strong spectral overlap between QD photoluminescence and SnS2 optical absorption as well as the large nominal donor-acceptor interspacing between QD core and SnS2. We also find enhanced charge carrier mobility in hybrid QD-SnS2 FETs which we attribute to a reduced contact Schottky barrier width due to an elevated background charge carrier density.