By employing aerobic oxidation to aldehydes as a more effective alcohol activation strategy, we developed a green Cu-catalyzed N-alkylation method for various amides and amines with alcohols. This reaction is more advantageous than the literature methods for it uses a ligand-free copper catalyst, can be readily carried out under milder aerobic conditions and generates water as the only byproduct. More importantly, based on our mechanistic studies and also supported by the literature, rather than following the previously-proposed mechanisms, we deduce that the newly-proposed relay race process should be the most possible and a more rational mechanism for the reactions, especially under aerobic conditions.