The three-bed temperature swing adsorption (TSA) air prepurification unit (APU) was proposed instead of the two-bed one. The three-bed TSA-APU can make energy savings of 29.5% by recovering and reusing the effluent purge gas. However, unlike the two-bed TSA-APU purged by clean gas, the impurities in the recovered gas may influence the bed performance. This study aimed to understand this influence by numerical simulation. Based on a nonequilibrium, nonisothermal, and nonadiabatic mathematic model, the breakthrough curves and bed profiles were obtained. The adsorption breakthrough curves show that the impurity contents in the product air of the three-bed TSA-APU are much lower than the typical tolerable limits. Thus, the energy savings of a TSA-APU were achieved by the three-bed design. The mechanisms that lead to this result were also discussed by analyzing the location and nature of the mass transfer and plateau zones, which were identified from the bed profiles.