Based to the first-principles calculations, we study the electronic properties of graphene/MoS2 heterostructure by modulating the vertical strains and applying external electric field. Graphene/MoS2 heterostructure is a van der Waals heterostructure (vdWH) with the interlayer spacing is 3.2 Å for the equilibrium state, and the contact property of the interface is n-type Schottky contact. The Schottky barrier height (SBH) changes with vertical strains which induces a change of charge transfer between graphene and MoS2 layer. In addition, with strain or without strain, the applied positive electric field can effectively promote the charge transfer from graphene to MoS2, while the negative electric field has the opposite effect. These findings support for the design of field effect transistors based on graphene vdWHs. Display omitted .The interface contact properties of graphene/MoS2 heterostructure are modulated by strains and applied electric field, which contributes to the development of new nano electronic devices. •The electronic properties of graphene/MoS2 can be modulated via strain and electric field.•Schottky barrier height is determined by charge transfer between graphene and MoS2 layers.•These findings support for the design of field-effect transistors based on graphene vdWHs.