O atoms segregate to the surface during Cu homoepitaxial growth on Cu(001)-(2√2×√2)-O to retain the (2√2×√2) surface. The presence of adsorbed O atoms on the Cu surface suppresses the surface diffusivity of Cu adatom and the growth proceeds by site-exchange between Cu adatoms and adsorbed O atoms, which heightens the transition temperature of the growth mode from step-flow to layer-by-layer. There exists a critical Cu deposition rate above which the O atoms can not exchange the site with Cu adatoms. The critical Cu deposition rate obeys an Arrhenius relation and the activation energy for the site-exchange is estimated at 0.66eV.