The catalytic reduction of NO by CO at Pd surfaces is studied using density functional theory. The reaction pathways and energy barriers of the elementary reaction steps are calculated at four different Pd surfaces: Pd(111), Pd(100), stepped Pd(211), and edged, missing-row reconstructed Pd(311). The stability of the reaction intermediates, chemisorbed NO, CO, N-2, N, and O, varies only moderately with the Pd surface structure. The energy barriers for the elementary reaction steps vary, however, more strongly with the Pd structure. The energy barriers for NO dissociation and for N-2 association are found to be much smaller at palladium steps and edges compared to the values at flat Pd(111) and Pd(100). For the CO2 formation, steps and edges have little influence on the energy barrier, reflecting that the flat Pd(100) surface already contains a very favorable ensemble for the CO2 formation.