The structural and electronic properties of black phosphorus/MoS₂ (BP/MoS₂) van der Waals (vdW) heterostructure are investigated by first-principles calculations. It is demonstrated that the BP/MoS₂ bilayer is a type-II p-n vdW heterostructure, and thus the lowest energy electron–hole pairs are spatially separated. The band gap of BP/MoS₂ can be significantly modulated by external electric field, and a transition from semiconductor to metal is observed. It gets further support from the band edges of BP and MoS₂ in BP/MoS₂ bilayer, which show linear variations with E_⊥. BP/MoS₂ bilayer also exhibits modulation of its band offsets and band alignment by E_⊥, resulting in different spatial distribution of the lowest energy electron–hole pairs. Our theoretical results may inspire much interest in experimental research of BP/MoS₂ vdW heterostructures and would open a new avenue for application of the heterostructures in future nano- and optoelectronics.