We have systematically investigated, by using scanning tunneling microscopy, the adsorption and film growth of C-60 on the various GaAs(001) surface phases prepared by molecular-beam epitaxy. For most phases, the C-60 overlayer exhibits the usual close-packed fcc(111) configuration with its lattice constant close to that of the bulk C-60 crystal. However, in the case of C-60 on the As-rich 2 X 4 substrate, the epitaxial growth is found to be quite different and unique; C-60 film takes its (110) crystalline axis; the C-60 overlayer is highly strained with a lattice expansion of similar to 13%, and this structure is very stable at least up to 10 ML. We will address the underlying formation mechanism of this new structure in terms of a charge transfer from the As-dangling bonds to C(60)s and a site-specific C-60-substrate interaction, as confirmed by molecular dynamic simulations. The present system provides a unique opportunity to study fullerene and/or noble-gas related two-dimensional phenomena, and demonstrates a potential for fabrication of novel fullerene-based devices, such as strained superlattice structures.