Infrared photodetectors based on single-layer CVD-grown graphene and PbS quantum dots, which are fabricated by solution processing, show ultrahigh responsivities of up to 10(7) A/W under infrared light illumination. The devices fabricated on flexible plastic substrates have excellent bending stability. The photoresponse is attributed to the field-effect doping in graphene films induced by negative charges generated in the quantum dots.