A promising BP/SnSe van der Waals (vdW) photovoltaic heterostructure was designed and investigated by first-principles calculations. The BP/SnSe vdW heterostructure showed inhibition of photogenerated carrier recombination as well as broad and high optical absorption intensity spanning the visible to deep ultraviolet regions reaching the order of 105 cm-1. The carrier mobility of the BP/SnSe vdW heterostructure exhibited anisotropic characteristics reaching approximately 103 cm2 V-1 s-1, with an intrinsic power conversion efficiency (PCE) of 11.96%. Our results show that the PCE can be increased to 17.24% when the conduction band offset between BP and SnSe is reduced by strain engineering. The distinctive and favorable properties suggest that the BP/SnSe vdW heterostructure has great potential for use in photovoltaic devices.