The surface areas and uptake of CO2 and CH4 by four graphene samples are measured and compared with activated charcoal. The surface areas are in the range of 5–640 m2 g−1, whereas the CO2 and CH4 uptake values are in the range of 18–45 wt % (at 195 K, 0.1 MPa) and 0–2.8 wt % (at 273 K, 5 MPa), respectively. The CO2 and CH4 uptake values of the graphene samples vary linearly with the surface area. In contrast, graphene-like BxCyNz samples with compositions close to BC2N exhibit surface areas in the range of 1500–1990 m2 g−1 and CO2 and CH4 uptake values in the ranges 97–128 wt % (at 195 K, 0.1 MPa) and 7.5–17.3 wt %, respectively. The uptake of these gases varies exponentially with the surface area of the BxCyZn samples, and the uptake of CH4 varies proportionally with that of CO2. The uptake of CO2 for the best BC2N sample is 64 wt % at 298 K. The large uptake of both CO2 and CH4 gases by BC2N betters the performance of graphenes and activated charcoal. First-principles calculations show that the adsorption of CO2 and CH4 is more favored on BCN samples compared to graphene.