The emergence of auction that supports bids characterized by several attributes is one of the most recent evolutions within auction theory. The purpose of this paper is to introduce multi-attribute into the on-line auction mechanism, proposed by Lavi and Nisan. Our mechanism is designed for auctioning multiple units of a good when the bidders arrive and depart dynamically. To incorporate the buyer’s preferences across attributes in an auction setting, we adopt a novel application of a scoring function. Furthermore, we describe a competitive reservation utility strategy (RUS), which helps the buyer decide when and how many goods he should buy. Finally, we also perform numerical examples showing our results.