A copper-phthalocyanine (CuPc) thin film was heteroepitaxially grown by the organic molecular beam epitaxy method at 200 degreesC on an indium-tin oxide (ITO) film with an atomically flat terraced and stepped surface. Two different epitaxial domains with a 6-fold symmetry of CuPc were grown on the ITO substrate with relationships of (100){001}CuPc parallel to (111){112}ITO (major domain) and (100){001}CuPc parallel to (111){110}ITO (minor domain). The orientation of the major domain was better than that of the minor domain. The difference in orientation may be understood by considering geometrical matching between the CuPc molecules and the ITO surface.