The Nb films with thickness from several tens to 500 Angstrom were grown by means of a special evaporation source (NbEBES) on (0001) alumina substrates in ultra high vacuum (UHV) conditions. The quality of the substrate surface and epitaxial parameters of the Nb over layers were examined by Reflection High Energy Electron Diffraction (RHEED). The two epitaxial orientations of Nb film with respect to the (0001) surface plane of alumina substrate were observed in the dependence of the substrate temperature during the Nb deposition. In the range between 250 and 400 degrees C the (110) epitaxial orientation was found. For the substrate temperature higher than 400 degrees C the (111) epitaxial orientation took place. Also the influence of the substrate temperature on the surface roughness of the resulted Nb film was studied. Very low evaporation rate (several Angstrom/min) at the substrate temperature range between 350 and 400 degrees C produced a relatively smooth surface of the Nb thin film with the (110) epitaxial orientation.