The family of carbon allotropes (graphene, carbon nanotube) with its rich chemistry and physics, attracts a great deal of attentions in forming novel hybrid nanostructures. However, owing to the low absorption, the performance of pristine graphene and carbon nanotube photodetectors are greatly limited. Combining low-dimensional nanomaterials into hybrid nanostructures is a promising avenue to obtain enhanced material properties and to achieve nanodevices operating with novel principles. Here we demonstrate a photodetector based on carbon nanotube/graphene doped with P3HT. A broadband photodetector (covering 405-980 nm) based on such hybrid films is fabricated with a high photoresponsivity of above 104 A/W. The results presents a potential application for efficient, low-cost, scalable vis-IR photodetection for all-carbon based photodetectors.