Band structure engineering in a MoS₂/PbI₂ van der Waals (vdW) heterostructure under an external electric field (E_field) is investigated using density functional theory (DFT). It is demonstrated that the MoS₂/PbI₂ vdW heterostructure has a type-II heterojunction with a direct bandgap, and thus the lowest energy electron–hole pairs are spatially separated. Meanwhile, the band structure could be effectively modulated under an E_field and the bandgap shows linear variations with the E_field, indicating a giant Stark effect. This gets further support from the band edges of MoS₂ and PbI₂ in the heterostructure. Moreover, the MoS₂/PbI₂ vdW heterostructure experiences transitions from type-II to type-I and then to type-II under various E_fields. Our calculated results pave the way for experimental research and provide a new perspective for the application of the vdW heterostructure in electronic and optoelectronic devices.