van der Waals (vdW) heterostructures formed by stacking different two-dimensional layered materials have been demonstrated as a promising platform for next-generation photonic and optoelectronic devices due to their tailorable band-engineering properties. Here, we report a high photoresponsivity and broadband photodetector based on a WSe2/SnSe2 heterostructure. By properly biasing the heterostructure, its band structure changes from near-broken band alignment to type-III band alignment which enables high photoresponsivity from visible to telecommunication wavelengths. The highest photoresponsivity and detectivity at 532 nm are ∼588 A W-1 and 4.4 × 1010 Jones and those at 1550 nm are ∼80 A W-1 and 1.4 × 1010 Jones, which are superior to those of the current state-of-the-art layered transition metal dichalcogenides based photodetectors under similar measurement conditions. Our work not only provides a new method for designing high-performance broadband photodetectors but also enables a deep understanding of the band engineering technology in the vdW heterostructures possible for other applications, such as modulators and lasers.