Molecular Dynamics simulations were performed to study Cu film deposition on β-Ta. Three different β-Ta surfaces were used, two being atomically flat, and one resulting from Ta on Ta growth. We find that the Cu films develop a (111) texture with vertical grain boundaries between grains having different epitaxial relations with the β-Ta substrate. The epitaxial rotation angles were determined, as 5.2° and 10-13°, and the resulting strain reductions in the Cu films were identified. The effects of the substrate differences on the interfacial Ta/Cu intermixing and the epitaxy and grain boundary structure of the films are discussed.