van der Waals heterostructures provide a powerful platform for engineering the electronic properties and for exploring exotic physical phenomena of two-dimensional materials. Here, we construct a graphene/BSe heterostructure and examine its electronic characteristics and the tunability of contact types under electric fields. Our results reveal that the graphene/BSe heterostructure is energetically, mechanically, and thermodynamically stable at room temperature. It forms a p-type Schottky contact and exhibits a high carrier mobility, making it a promising candidate for future Schottky field-effect transistors. Furthermore, applying an electric field not only reduces contact barriers but also induces a transition from a p-type to an n-type Schottky contact and from a Schottky to an ohmic contact, offering further potential for the control and manipulation of the heterostructure's electronic properties. Our findings offer a rational basis for the design of energy-efficient and tunable heterostructure devices based on the graphene/BSe heterostructure.