Two-dimensional (2D) atomic crystals, such as graphene, black phosphorus and transition metal dichalcogenides (TMDCs) are attractive for use in optoelectronic devices, due to their unique optical absorption properties and van der Waals (vdWs) force between layers. Heterostructures based on layered semiconductors provide a new platform for broadband high-performance photodetectors. In this work, graphene-MoTe2-WS2-graphene vdWs heterojunctions are fabricated for photodetection. The fundamental electric properties and the band structures of the heterojunctions are investigated and discussed. The devices show a high responsivity (≈ 140 mA W -1 at 825 nm), stable and broadband photodetection from UV to NIR wavelength range (300 - 1350 nm), fast response time of 186 µs and self-driven photodetectors. The scanning photocurrent microscopy maps are also employed to study the mechanism of photocurrent generation in the heterojunction. Our results reveal that the vdWs heterojunctions with graphene electrodes offer a new route to broadband detection, optical communication and energy harvesting applications.