Passive NOx, adsorption using zeolite supported Pd catalysts has been considered one of most effective methods for low-temperature NO storage in the diesel engine emission control. In the present work, first-principles density functional theory calculations were used to study NO adsorption at the highly dispersed Pd sites, i.e., monomeric (PdO)-O-II and dimeric [Pd-II-O-Pd-II](2+) in the HBEA zeolite. It has been found that each (PdO)-O-II and [Pd-II-O-Pd-II](2+) sites could bind with three and four NO molecules, respectively. Upon adsorption, NO could be oxidized to NO2, resulting in the reduction of Pd-II to Pd-0 for (PdO)-O-II and Pd-II to Pd-I, for [Pd-II-O-Pd-II](2+) respectively. With increasing NO coverage at both sites, NO oxidation becomes more facile with low activation barriers of 13 and 22 kJ/mol. At the [Pd-II-O-Pd-II](2+) site, the binding of formed NO2 becomes weak at high NO coverage. Both (PdO)-O-II and [Pd-II-O-Pd-II](2+) sites are protonated to the more stable [(PdOH)-O-II](+) and [(PdOH)-O-II](+)/[(PdOH)-O-II](+) sites in the presence of H2O or neighboring BAS sites. Finally, we studied the CO effect on the NO adsorption in Pd/HBEA. With co-fed CO in the NOx, mixture, both (PdO)-O-II and [Pd-II-O-Pd-II](2+) could be reduced to Pd degrees and [Pd-I-Pd-I](2+) sites. Compared to the NO adsorption, our calculations show that CO adsorption is slightly stronger at the (Pd-II-O-Pd-II)(2+) site while it is slightly weaker at the (PdO)-O-II site. CO oxidation, rather than NO oxidation readily occurs if NO and CO co-adsorbed. The reduced Pd-I site and the [(PdOH)-O-II](+)/[(PdOH)-O-II](+) site enhances NO adsorption.