Graphene has emerged as a promising material for photonic applications fuelled by its superior electronic and optical properties. However, the photoresponsivity is limited by the low absorption cross-section and ultrafast recombination rates of photoexcited carriers. Here we demonstrate a photoconductive gain of ∼10(5) electrons per photon in a carbon nanotube-graphene hybrid due to efficient photocarriers generation and transport within the nanostructure. A broadband photodetector (covering 400-1,550 nm) based on such hybrid films is fabricated with a high photoresponsivity of >100 A W(-1) and a fast response time of ∼100 μs. The combination of ultra-broad bandwidth, high responsivities and fast operating speeds affords new opportunities for facile and scalable fabrication of all-carbon optoelectronic devices.