In this work, we construct an ultrathin graphene/GaS heterostructure and investigate its electronic properties as well as the effect of vertical strain using density functional theory. The calculated results of the equilibrium interlayer spacing (3.356 Å) and the binding energy show that the intrinsic properties of isolated graphene and GaS monolayers can be preserved and the weak van der Waals interactions are dominated in the heterostructures. The van der Waals heterostructure (vdWH) forms an n-type Schottky contact with a small Schottky barrier height of 0.51 eV. This small Schottky barrier height can also be tuned by applying vertical strain. Furthermore, we find that the n-type Schottky contact of the vdWH can be changed to p-type when the interlayer spacing is decreased and exceeded to 2.60 Å. These findings show the great potential application of the graphene/GaS vdWH for designing next generation devices.