Epitaxial (Ill)-oriented C-60 films have been grown on alkali-halide substrates, KCI (100), KBr (100) and NaCl (100) by a three-step process: (1), substrate surface cleaning by high temperature heating; (2), initial deposition with a low deposition rate to grow two or three monolayers (ML); and (3), deposition with a high deposition rate to grow a film with expected thickness. It was found that (Ill)-oriented epitaxial C-60 films could be grown at low temperatures in a wide temperature range, from 40 to 120 degrees C. By this three-step process, we can also grow epitaxial C-60 films at deposition rates as high as 35 Angstrom/min.