The effects of support on gas adsorption is crucial for single atom catalysts design and optimization. To gain insight into support effects on gas adsorption characteristics, a comprehensive theoretical study was performed to investigate the adsorption characteristics of toxic gases (NO2, NH3, SO3 and H2S) by utilizing single atom iron catalysts with three graphene-based supports. The adsorption geometry, adsorption energy, electronic and magnetic properties of the adsorption system have been explored. Additionally, the support effects have been analyzed through d-band center and Fermi softness, and thermodynamic analysis has been performed to consider the effect of temperature on gas adsorption. The support effects have a remarkable influence on the adsorption characteristics of four types of toxic gases which is determined by the electronic structure of graphene-based support, and the electronic structure can be characterized by Fermi softness of catalysts. Fermi softness and uplift height of Fe atom could be good descriptors for the adsorption activity of single atom iron catalysts with graphene-based supports. The findings can lay a foundation for the further study of graphene-based support effects in single atom catalysts and provide a guideline for development and design of new graphene-based support materials utilizing the idea of Fermi softness. (C) 2017 Elsevier B.V. All rights reserved.