Here, we present a detailed computational study of the stability and the electronic structure of nitrogen-doped graphene (N 4 V 2 ) supported Cu n (n = 1−5) clusters, which are promising carbon-dioxide electroreduction catalysts. The binding of the clusters to the nitrogen-doped graphene and the electronic structure of these systems were investigated under vacuum and electrochemical conditions. The stability analysis showed that among the systems, the nitrogen-doped graphene bound Cu 4 is the most stable in vacuum, while in an electrolyte, and at a negative potential, the N 4 V 2 −Cu 3 is energetically more favorable. The ground state electronic structure of the nitrogen-doped graphene substrate undergoes topological phase transition, from a semimetallic state, and we observed a metallic and topologically trivial state after the clusters are deposited. The electrode potential adjusts the type and density of the charge carriers in the semimetallic models, while the structures containing copper exhibit bands which are deformed and relaxed by the modified number of electrons.