Although graphene-based heterostructures exhibit excellent intrinsic properties for device scaling, fabricating low Schottky barrier is still a great challenge to the electrical transport behaviors of nanoelectronic devices. Exploring excellent materials for electronic devices are a research hotspot at present. Graphene not only exhibits excellent physical strength and specific surface area, but also presents high carrier mobility and thermal conductivity. Therefore, graphene has been developed in many fields such as energy, catalysis, etc. However, graphene is a special material with zero band gap, and its electrons and holes are easy to compound, which seriously hinders its development in the applications of electronic and optoelectronic devices. Two-dimensional transition metal dichalcogenides (TMDs) have the advantages of controllable band gap properties, which makes them have a good development in logic circuits and photodetectors. As one of TMD_S, MoSe₂ possesses the advantages of narrower band gap, better electron hole separation and stronger oxidation resistance in the environment. Therefore, the design of graphene and MoSe₂ heterostructures is an ideal choice for a new generation of nanoelectronic devices. Here, we investigate systematically the effects of asymmetric O doping on the electronic properties and Schottky barrier of graphene/MoSe_2(1–x)O_2x heterostructure for the first time by first-principles calculations incorporating semiempirical dispersion-correction scheme. The results indicate that graphene and MoSe₂ monolayer can form a stable van der Waals heterostructure with preserving their own intrinsic properties. In addition, an n-type schottky contact with a barrier height of 0.558 eV is obtained. Further, it is found that the type and the height of the Schottky barrier can be controlled by changing the concentration and sites of the O dopant at interface. By increasing the concentration of the O dopant inside the interface, the transition from an n-type Schottky contact to an Ohmic contact can be realized, and a low n-type Schottky barrier is gained with increasing the concentration of the O dopant outside the interface for highly efficient charge transfer. The barrier height of heterostructure decreases from 0.558 eV to 0.112 eV when the O dopant is doped on the outer interface. Finally, as a complement to previous results, it is confirmed that the redistribution of interfacial charges leads the Fermi level to shift, and thus determining the type and the height of Schottky barrier. This study may provide theoretical guidance for designing and manufacturing the MoSe₂-based nano field effect transistors.