The future development of optoelectronic devices will require an advanced control technology in electronic properties, for example by an external electric field (E_field). Here we demonstrate an approach that the heterostructure based on van der Waals (vdW) heterobilayer built by monolayer SnS₂ and PbI₂ has a well-controlled electronic properties with E_field. A type-II staggered-gap band alignment is achieved from the SnS₂/PbI₂ vdW heterostructure with which SnS₂ dominated the lowest energy holes as well as the lowest energy electrons are separated in PbI₂. The charge redistribution with an E_field is mainly on the surface of SnS₂ layer and PbI₂ and the numbers of polarized electrons on the monolayers display a linear evaluation with external E_field. The band structure under different E_field experiences not only a transition from semiconductor to metal but also conversions between type-I straddling-band alignment and type-II staggered-gap, which results in different spatial distribution of the lowest energy electrons and holes. Moreover, when the E_field is between −0.06 V Å⁻¹ and −0.34 V Å⁻¹, the material manifests a varied direct bandgap which is more favor to optoelectronics and solar cell. Consequently, this vdW heterobilayer with well-controlled manner shows expectation for huge potential in optics and electronics.