The sustainable generation of H-2 from water electrolysis is a promising approach to alleviating current energy crisis and environmental pollution. However, the efficiency of such a system is limited by the conventional noble metal catalysts. Herein, using first-principle calculations, we demonstrate the potential of non-precious Co- and N-codoped graphene systems (CoNx-N/O-gra, x = 1-4) in efficiently catalyzing the hydrogen evolution reaction (HER). The findings showed that the activity of the Co sites was influenced by the concentration and configuration of N dopants, as well as the coordination environment of Co atom. From the volcano curve, obtained by plotting the exchange current as a function of the adsorption free energy, optimal performance was achieved on CoN4-gra, which was attributed to the moderate adsorption of CoN4-gra towards H. The electronic structures analyses confirmed that the hybridization between Co sp orbital and H s orbital played key role in tuning the interactions between the catalysts and H, which could be regulated by the coordination environment of Co. The present findings highlight the potential of non precious metal/non-metal-codoped graphene as HER catalysts and offers an effective approach to tune the HER activity by modifying the coordination environment of the metal atoms. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.