Towards a sustainable carbon cycle, electrochemical conversion of CO2 into valuable fuels has drawn much attention. However, sluggish kinetics and a substantial overpotential, originating from the strong correlation between the adsorption energies of intermediates and products, are key obstacles of electrochemical CO2 conversion. Here we show that two-dimensional (2D) covalent metals with a zero band-gap can overcome the intrinsic limitation of conventional metals and metal alloys and thereby substantially decrease the overpotential for CO2 reduction because of their covalent characteristics. From first-principles-based high-throughput screening results on 61 2D covalent materials, we find that the strong correlation between the adsorption energies of COOH and CO can be entirely broken. This leads to the computational design of CO2-to-CO and CO2-to-CH4 conversion catalysts in addition to hydrogen-evolution-reaction catalysts. Towards efficient electrochemical catalysts for CO2 reduction, this work suggests a new materials domain having two contradictory properties in single material; covalent nature and electrical conductance.