We have fabricated ZnO thin films on sapphire substrates at temperatures ranging from 350 to 1000 degrees C by laser molecular-beam epitaxy. With increasing growth temperature, lateral grain size evaluated by X-ray reciprocal space mapping increased resulting in improved electron mobility. When the film was grown at 1000 degrees C, an electron mobility as large as 90 cm(2)/Vs was achieved. By annealing in 1 atm of oxygen at 1000 degrees C, thin films having much larger grain size (> 5 mu m(2)) and higher mobility(similar to 120 cm(2)/V s) comparable with those for bulk single crystals could be obtained.