Interfacial interactions and electronic properties of graphene/CH3NH3PbI3 heterojunctions were investigated by first-principles calculations incorporating semiempirical dispersion-correction scheme to describe van der Waals interactions. Two lattice match configurations between graphene and CH3NH3PbI3(001) slab were constructed in parallel contact and both of them were verified to form remarkable van der Waals heterojunctions with similar work functions. Our calculated energy band structures show that the Dirac-cone of graphene and the direct band gap of CH3NH3PbI3 are still preserved in the heterojunctions, thus graphene can be a promising candidate either as a capping or supporting layer for encapsulating CH3NH3PbI3 layer. It is identified that the Schottky barrier of graphene/CH3NH3PbI3 heterojunctions can be controlled by the interlayer distance and affected by the stacking pattern of graphene and CH3NH3PbI3. The 3D charge density differences present the build-in internal electric field from graphene to CH3NH3PbI3 after interface equilibrium and thus, a low n-type Schottky barrier is needed for high efficient charge transferring in the interface. The possible mechanism of the band edge modulations in the heterojunctions and corresponding photoinduced charge transfer processes are also described. (C) 2018 Elsevier B.V. All rights reserved.