Recent exciting developments in synthesis and properties study of the Germanane (GeH) monolayer have inspired us to investigate the structural and electronic properties of the van der Waals GeH/Graphene (Gr) heterostructure by the first-principle approach. The stability of the GeH/Gr heterostructure is verified by calculating the phonon dispersion curves as well as by thermodynamic binding energy calculations. According to the band structure calculation, the GeH/Gr interface is n-type Ohmic. The effects of different interlayer distances and strains between the layers and the applied electric field on the interface have been investigated to gain insight into the van der Waals heterostructure modifications. An interlayer distance of 2.11 angstrom and compressive strain of 6% alter the contact from Ohmic to Schottky status, while the electric field can tune the GeH/Gr contact as p- or n-type, Ohmic, or Schottky. The average electrostatic potential of GeH/Gr and the Bader charge analysis have been used to explain the results obtained. Our theoretical study could provide a promising approach for improving the electronic performance of GeH/Gr-based nano-rectifiers.