The adsorption and diffusion of Ge adatoms and ad-dimers on the one-monolayer Sb-covered Si(001) surface are studied using first-principles total-energy calculations. It is shown that Ge adatoms and ad-dimers can both break Sb dimers because of the weak bonding of the Sb dimers on Si(001). As a result, the most stable sites are both on the Sb dimer rows for Ge adatoms and ad-dimers, which is in significant contrast to the conventional picture that the most stable site for a Ge ad-dimer is in the trough between the group-V element dimer rows. We have also examined the energetics of the site exchange between Ge and Sb atoms for the surfactant-mediated growth and find that Ge ad-dimers tend to exchange with the subsurface Sb atoms one by one perpendicular to the surface dimer rows.