We have fabricated UV-sensitive photodetectors based on colloidal CdS nanocrystals and graphene. The nanocrystals act as a sensitizer layer that improves light harvesting leading to high responsivity of the detector. Despite the slow relaxation of the photogenerated charges in the nanocrystal film, faster processes allowed to detect pulses up to a repetition rate of 2 kHz. We have performed time-resolved analysis of the processes occurring in our hybrid system, and discuss possible photo-induced charge transfer mechanisms.