The platinum copper alloy nanocrystals (NCs) have generated much interest because of their wide applications in fuel cells due primarily to their good catalytic performance and to decreasing sensitivity toward CO poisoning. The exact atomic-level morphology of platinum copper alloy NCs is still not clear in the literature, and research to understanding the poisoning mechanism is still insufficient to date. In this article, we report on density functional calculations of small PtnCu clusters and their adsorption of a CO molecule that provide evidence for degrading adsorption of the CO molecule compared to pure platinum clusters. The lowest-energy geometries of PtnCu and PtnCuCO clusters have been identified. The CO molecule prefers to be adsorbed on the nearest platinum atom by the C-end-on mode, forming linear or quasi-linear O-C-Pt structures. The adsorption energies indicate that the introduction of a copper atom decreases the adsorption ability of the CO molecule. The local density of states of the representative clusters is used to characterize the adsorption properties of the CO molecule on the PtnCu clusters. Results from our theoretical calculations can be helpful for understanding the poisoning mechanism of the CO molecule on the platinum copper alloy NCs.