This paper presents a new false-name-proof multi-unit auction protocol called Greedy ALlocation (GAL) protocol. Internet auctions have become an integral part of Electronic Commerce and a promising field for applying agent and Artificial Intelligence technologies. Although the Internet provides an excellent infrastructure for executing auctions, the possibility of a new type of cheating called false-name bids has been pointed out. A false-name bid is a bid submitted under a fictitious name. A protocol called Iterative Reducing (IR) protocol has been developed for multi-unit auctions and has proven to be false-name-proof, i.e., using false-name bids is useless. For Internet auction protocols, being false-name-proof is important since identifying each participant on the Internet is virtually impossible. One shortcoming of the IR protocol is that it requires the auctioneer to carefully pre-determine the reservation price for one unit. Our newly developed GAL protocol is easier to use than the IR, since the auctioneer does not need to set the reservation price nor any other parameters. The evaluation results show that the GAL protocol can obtain a social surplus that is very close to Pareto efficient. Furthermore, the obtained social surplus and seller’s revenue are much better than those of the IR protocol even if the reservation price is set optimally.