We have systematically investigated, by using scanning tunneling microscopy, the adsorption and film growth ofC60on the various GaAs(001) surface phases prepared by molecular-beam epitaxy. For most phases, theC60overlayer exhibits the usual close-packed fcc(111) configuration with its lattice constant close to that of the bulkC60crystal. However, in the case ofC60on the As-rich2×4substrate, the epitaxial growth is found to be quite different and unique;C60film takes its (110) crystalline axis; theC60overlayer is highly strained with a lattice expansion of∼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 toC60sand a site-specificC60-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.