In the first ever attempt to study the adsorption of organic molecules on high-index Si surfaces, we investigated the adsorption of benzene on Si(5 5 12)-(2x1) by using variable-low-temperature scanning tunneling microscopy and density-functional theory (DFT) calculations. Several distinct adsorption structures of the benzene molecule were found. In one structure, the benzene molecule binds to two adatoms between the dimers of D3 and D2 units in a tilted butterfly configuration. This structure is produced by the formation of di-sigma bonds with the substrate and of two C[Double Bond]C double bonds in the benzene molecule. In another structure, the molecule adsorbs on honeycomb chains with a low adsorption energy because of strain effects. Our DFT calculations predict that the adsorption energies of benzene are 1.03-1.20 eV on the adatoms and 0.22 eV on the honeycomb chains.