Van der Waals heterostructures, created by putting graphene on other two-dimensional semiconducting materials, have become an effective strategy to enhance the physical properties and extend the possible applications of two-dimensional (2D) materials. Motivated by the successful synthesis of a graphene/PbI2 heterostructure in a recent experiment [Nat. Commun. 11, 823 (2020)], here we use first-principles calculations to construct and investigate the electronic properties and interface characteristics of graphene/PbI2 heterostructure. We find that the weak forces occurring at the interface keep heterostructures stable and maintain the intrinsic properties of the constituent graphene and PbI2 monolayers. At the equilibrium interlayer distance of 3.48 Å, the graphene/PbI2 heterostructure forms an n-type Schottky contact. More interestingly, the Schottky barrier height and contact types in the graphene/PbI2 heterostructure can be adjusted by electric field and interlayer coupling. The graphene/PbI2 heterostructure can transform from a n-type Schottky contact to a p-type one or to Ohmic contact by applying electric field or by adjusting interlayer distance. The controllable electronic properties and contact types in graphene/PbI2 heterostructure make it a promising candidate for designing and improving the performance of high-efficiency Schottky nanodevices.