Intensive studies have recently been performed on graphene-based photodetectors, but most of them are based on field effect transistor structures containing mechanically exfoliated graphene, not suitable for practical large-scale device applications. Here we report high-efficient photodetector behaviours of chemical vapor deposition grown all-graphene p-n vertical-type tunnelling diodes. The observed photodetector characteristics well follow what are expected from its band structure and the tunnelling of current through the interlayer between the metallic p- and n-graphene layers. High detectivity (~10(12) cm Hz(1/2) W(-1)) and responsivity (0.4~1.0 A W(-1)) are achieved in the broad spectral range from ultraviolet to near-infrared and the photoresponse is almost consistent under 6-month operations. The high photodetector performance of the graphene p-n vertical diodes can be understood by the high photocurrent gain and the carrier multiplication arising from impact ionization in graphene.