Single-oriented pure phase CuGaO2 and CuGa2O4 films have been successfully grown on β-Ga2O3 (2¯01) substrate by reactive deposition epitaxy at different oxygen partial pressures. Oxygen partial pressure-controlled mass-transport of Cu atoms is the dominant controlling parameter for CuGaO2 and CuGa2O4 growth. As the oxygen partial pressure increases, the amount of Cu atoms diffused in to the substrate surface under the control of mass-transport increases gradually and the Cu/Ga atomic ratio involved in the reaction progressively decreases, resulting in the product changing from CuO and CuGaO2 to CuGa2O4. After Chemical-mechanical Polishing (CMP) treatment, the CuGaO2 and CuGa2O4 films show pure phase with narrow full-width half-maximum (FWHM) according to high-resolution X-ray diffraction (HR-XRD). In addition, the transmission electron microscopy (TEM) results indicated better interface quality and epitaxial relationship between Cu-Ga-O films and β-Ga2O3 substrate. The smooth surface of Cu-Ga-O films can be obtained after CMP treatment which is confirmed by atomic force microscopy (AFM) results. It presents a feasible route to prepare β-Ga2O3-based heterojunction via reactive deposition epitaxy to expand the application of β-Ga2O3 in ultraviolet detection and power devices.