In this study, graphite, graphene, and hydrophilic-treated graphene electrodes were evaluated in a dual-chamber microbial fuel cell (DC-MFC). Free-oxygen conditions were promoted in anodic and cathodic chambers. Hydrochloric acid at 0.1 M and pH 1.1 was used as a catholyte, in addition to deionized water in the cathodic chamber. Domestic wastewater was used as a substrate, and a DuPontTM Nafion 117 membrane was used as a proton exchange membrane. The maximum power density of 32.07 mW·m−2 was obtained using hydrophilic-treated graphene electrodes and hydrochloric acid as catholyte. This power density was 1.4-fold and 32-fold greater than that of graphene (22.15 mW·m−2) and graphite (1.02 mW·m−2), respectively, under the same operational conditions. In addition, the maximum organic matter removal efficiencies of 69.8% and 75.5% were obtained using hydrophilic-treated graphene electrodes, for hydrochloric acid catholyte and deionized water, respectively. Therefore, the results suggest that the use of hydrophilic-treated graphene functioning as electrodes in DC-MFCs, and hydrochloric acid as a catholyte, favored power density when domestic wastewater is degraded. This opens up new possibilities for improving DC-MFC performance through the selection of suitable new electrode materials and catholytes.