Graphene-based van der Waals heterostructures are expected recently to design and fabricate many novel electronic and optoelectronic devices. The combination of the electronic structures of graphene and graphene-like GaSe monolayer (g-GaSe) in an ultrathin heterostructure has been realized experimentally, such as graphene/g-GaSe field effect transistor and dual Schottky diode device. In the present work, we investigate the electronic properties of the graphene/g-GaSe heterostructures under the applied electric field, in-plane strains, and interlayer coupling. Our results show that the electronic properties of the graphene/g-GaSe heterostructures are well preserved owing to a weak vdW interaction. Especially, a tiny band gap of 13 meV has opened in the presence of the g-GaSe monolayer. We found that the n-type Schottky contact is formed in the graphene/g-GaSe heterostructure with a Schottky barrier height of 0.86 eV, which can be efficiently modulated by applying the electric field, in-plane strains, and interlayer coupling. Furthermore, a transformation from the n-type to p-type Schottky contact is observed when the applied electric field is larger than 0.1 V/Å or the interlayer distance is smaller than 3.2 Å. Our results may provide helpful information to design and fabricate the future graphene-based vdW heterostructures, such as graphene/g-GaSe heterostructure and understand the physics mechanism in the graphene-based 2D vdW heterostructures.