Two-dimensional (2D) materials exhibit massive potential in research and development in the scientific world due to their unique electrical, optical, thermal and mechanical properties. Graphene is an earliest found two-dimensional material, which has many excellent properties, such as high carrier mobility and large surface area. However, single layer graphene has a zero band gap, which limits its response in electronic devices. Unlike graphene, the transition metal sulfides (TMDs) have various band structures and chemical compositions, which greatly compensate for the defect of zero gap in graphene. The WS₂ is one of the 2D TMDs exhibiting a series of unique properties, such as strong spin-orbit coupling, band splitting and high nonlinear susceptibility, which make it possess many applications in semiconducting optoelectronics and micro/nano-electronics. The 2D semiconductors along with semimetallic graphene are seen as basic building blocks for a new generation of nanoelectronic devices. In this way, the artificially designed TMD heterostructure is a promising option for ultrathin photodetectors. There are few reports on the physical mechanism of carrier mobility and charge distribution at the interface of WS₂/graphene heterostructure, by varying the interfacial distance of WS₂/graphene heterostructure to investigate the effect on the electronic properties. Here in this work, the corresponding effects of interface cohesive interaction and electronic properties of WS₂/graphene heterostructure are studied by first-principles method. The calculation results indicate that the lattice mismatch between monolayer WS₂ and graphene is low, the equilibrium layer distance d of about 3.42 for the WS₂/graphene heterostructure and a weak van der Waals interaction forms in interface. Further, by analyzing the energy band structures and the three-dimensional charge density difference of WS₂/graphene, we can identify that at the interface of the WS₂ layer there appears an obvious electron accumulation: positive charges are accumulated near to the graphene layer, showing that WS₂ is an n-type semiconductor due to the combination with graphene. Furthermore, the total density of states and corresponding partial density of states of WS₂/graphene heterostructure are investigated, and the results show that the valence band is composed of hybrid orbitals of W 5d and C 2p, whereas the conduction band is comprised of W 5d and S 3p orbitals, the orbital hybridization between W 5d and S 3p will cause photogenerated electrons to transfer easily from the internal W atoms to the external S atoms, thereby forming a build-in internal electric field from graphene to WS₂. Finally, by varying the interfacial distance for analyzing the Schottky barrier transition, as the interfacial distance is changed greatly from 2.4 to 4.2 , the shape of the band changes slightly, however, the Fermi level descends relatively gradually, which can achieve the transition from a p-type Schottky contact to an n-type Schottky contact in the WS₂/graphene. The plane-averaged charge density difference proves that the interfacial charge transfer and the Fermi level shift are the reasons for determining the Schottky barrier transition in the WS₂/graphene heterostructure. Our studies may prove to be instrumental in the future design and fabrication of van der Waals based field effect transistors.