Motivated by recent experimental reports of zirconium porous coordination networks (PCNs) [J. Am. Chem. Soc. 2012, 134, 14690-14693], which have demonstrated a good stability and CO2 adsorption capacity, we investigate the influence of flue gas impurities and functional groups on the performance of PCN frameworks in selective CO2 capture. Using a combination of grand canonical Monte Carlo (GCMC) simulations and first-principles calculations, we find that O2 and SO2 impurities in flue gas have a negligible influence on CO2 selectivity in all PCN frameworks. However, because of strong electrostatic interaction between H2O molecules and the framework, CO2 selectivity decreases in all PCN structures in the presence of water impurities in the flue gas. Our studies suggest that the PCN-59 framework can be a good candidate for selective CO2 separation from a predehydrated flue gas mixture.