Two-dimensional (2D) material-based van der Waals (vdW) heterostructures have recently attracted much attention because the combined merits of two 2D monolayers enable many novel applications in nanoelectronic and optoelectronic devices. The recently synthesized graphene/WSe₂ vdW heterostructures are especially appealing, and understanding the effect of structural imperfection on the electronic properties of the graphene/WSe₂ vdW heterostructures is important for their practical application. In this study, we used first-principles calculations to investigate the structural and electronic properties of a graphene monolayer stacked on a WSe₂ monolayer with various structural defects: two Se vacancies (WSe₂-V_di-Se) and W vacancy (WSe₂-V_W). After the structural defects were introduced, the calculated properties of the graphene/WSe₂ vdW heterostructure were significantly changed. Therefore, it is extremely important to prepare defect-free WSe₂ for the nanoelectronics applications with dedicated function. On the other hand, the artificial generation of defects may provide a new approach to tune the electronic properties of graphene/WSe₂ vdW heterostructures. Moreover, by varying the interlayer coupling or by applying a perpendicular electric field, it is possible to further modulate the electronic properties of graphene/WSe₂ and graphene/WSe₂-V_di-Se vdW heterostructures. These theoretical results are expected to provide useful guidelines for the design of novel nanodevices based on graphene/WSe₂ vdW heterostructures.