This study presents the efficiency of TSS and organic pollutants (BOD5 and COD) removal in a hybrid constructed wetland wastewater treatment plant (VF-HF type) with an aeration system. This study was conducted over 6 years (2017–2022) in a facility with a capacity of 4.5 m3/day located in southeastern Poland and designed to treat real domestic wastewater from a school building. The studied facility consists of a three-chambered septic tank, a pumping station with an aeration system, and two beds with vertical and horizontal flow planted with giant miscanthus and willow. As a result of artificial aeration, the dissolved oxygen concentration in wastewater after mechanical treatment increased significantly, by an average of 1.18 mg O2/L, and was negatively correlated with wastewater temperature. The cumulative pollutant removal effects of the treatment plant (primary settling tank + VFCW + HFCW) were 81% for TSS, 98% for BOD5, and 89% for COD. There was no statistically significant effect of aeration on the organic pollutant removal effects in the VF bed, and such an effect was found for the temperature of wastewater entering the VF bed. The TSS, BOD5, and COD removal effects in the VF bed and BOD5 in the VF-HF system were positively correlated with air temperature. The technological reliability of the treatment plant was 98% for TSS and 100% for BOD5 and COD. The use of artificial aeration of wastewater makes it possible to achieve high organic pollutant removal efficiency in SSF CWs and to compensate for limitations due to the reduction in the area of constructed wetland beds.