In a unit-demand multi-unit multi-item auction, an auctioneer is selling a collection of different items to a set of agents each interested in buying at most unit. Each agent has a different private value for each of the items. We consider the problem of designing a truthful auction that maximizes the auctioneer's profit in this setting. Previously, there has been progress on this problem in the setting in which each value is drawn from a known prior distribution. Specifically, it has been shown how to design auctions tailored to these priors that achieve a constant factor approximation ratio [2, 5]. In this paper, we present a prior-independent auction for this setting. This auction is guaranteed to achieve a constant fraction of the optimal expected profit for a large class of, so called, "regular" distributions, without specific knowledge of the distributions.