GaN epilayers are grown on (111) oriented single crystal diamond substrate by ammonia-source molecular beam epitaxy. Each step of the growth is monitored in situ by reflection high energy electron diffraction. It is found that a two-dimensional epitaxial wurtzite GaN film is obtained. The surface morphology is smooth: the rms roughness is as low as 1.3 nm for 2 x 2 mu m(2) scan. Photoluminescence measurements reveal pretty good optical properties. The GaN band edge is centred at 3.469 eV with a linewidth of 5 meV. These results demonstrate that GaN heteroepitaxially grown on diamond opens new rooms for high power electronic applications. (C) 2009 Elsevier B.V. All rights reserved.