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The feasibility of employing a moving-bed adsorption (MBA) process as a postcombustion carbon capture process was investigated using zeolite 13X as the adsorbent. The MBA process consists of an adsorption bed and two desorption beds, which are operated under different temperatures and pressures. Adsorbent particles circulate around the beds in a countercurrent direction to the gas flow in each bed. A high-efficiency heat integration scheme that recovers the heat of adsorption and reuses this energy as the heat of desorption was designed and implemented to minimize the energy requirements. A fixed-bed dehydration unit using MIL-101 (Cr) as the adsorbent was also designed for pretreatment of the flue gas and was incorporated as an integral part of the process. Models were established for predicting the operating energy for constituent process units from the dehydration to liquefaction stages, and the minimum energy requirement was calculated. The results indicated that the total energy demand per unit amount of CO2 removal in terms of the equivalent work was intermediate to those of the optimized piperazine- and monoethanolamine-based absorption processes. The regeneration energy, which accounts for only the capture process, except for the dehydration and liquefaction processes, was estimated to be less than half of those of the absorption processes. The sensitivity of the process performance to the CO2 selectivity and sorption capacity was also analyzed to investigate the potential improvement in the performance of the MBA process when using more efficient adsorbents.