Molybdenum carbide (Mo2C) based catalysts have been found to be one of the most promising catalysts for hydrogen evolution reaction (HER). As a first attempt to understand their prominent catalytic activity, different Mo2C based models are theoretically investigated, while their catalytic activities are compared with respect to existing experimental results. The first constructed model structures consist of small Mo2C clusters adsorbed on clean/nitrogen-doped graphene surfaces which have shown an improvement in the HER activity compared with pristine graphene and Mo2C bulk. Regarding the cluster structure as a simplified representation of an active side on the cathode in the electrochemical cell, the HER is investigated using the density functional theory (DFT). This small cluster study is designed to give a qualitative insight into the HER catalysis of Mo2C nanoparticles and also to show guidance for a new catalyst design. We consider as well model structures consisting on a Mo2C (001) surface covered by pure and nitrogendoped (N-doped) graphene layers. This model surfaces show high HER activities in both acidic and alkaline electrolytes. The N-doped impurities in the graphene structures influence the HER activity. In this contribution the hydrogen adsorption at different active sites, the influence of the acidity on the HER activity and comparisons bewtween experimental and theoretical results are shown. Qualitatively, our theoretical results, based on a previously developed thermochemical approach, agree with recent experimental findings. (C) 2019 Elsevier Inc. All rights reserved.