Two-dimensional (2D) tin monoxide (SnO) has attracted much attention owing to its distinctive electronic and optical properties, which render itself suitable as a channel material in field effect transistors (FETs). However, upon contact with metals for such applications, the Fermi level pinning effect may occur, where states are induced in its band gap by the metal, hindering its intrinsic semiconducting properties. We propose the insertion of graphene at the contact interface to alleviate the metal-induced gap states. By using gold (Au) as the electrode material and monolayer SnO (mSnO) as the channel material, the geometry, bonding strength, charge transfer and tunnel barrier of charges, and electronic properties including the work function, band structure, density of states, and Schottky barriers are thoroughly investigated using first-principles calculations for the structures with and without graphene to reveal the contact behaviours and Fermi level depinning mechanism. It has been demonstrated that strong covalent bonding is formed between gold and mSnO, while the graphene interlayer forms weak van der Waals interactions with both materials, which minimises the perturbance to the band structure of mSnO. The effects of out-of-plane compression are also analysed to assess the performance of the contact under mechanical deformation, and a feasible fabrication route for the heterostructure with graphene is proposed. This work systematically explores the properties of the Au–mSnO contact for applications in FETs and provides thorough guidance for future exploitation of 2D materials in various electronic applications and for selection of buffer layers to improve the metal–semiconductor contact.