Electroreduction of carbon dioxide (CO₂) to useful chemical fuels represents an efficient and green strategy for solving the existing energy and environmental problems of human society. Developing efficient and inexpensive electrocatalysts for the CO₂ reduction reaction (CRR) has been a key scientific issue. Due to the robust scaling relationship that exists between CRR intermediates, it is difficult to improve the catalytic activity of commonly used transition metal catalysts. In this work, inspired by recent experimental progress in fabricating graphene-based dual-metal-site catalysts (DMSCs), we systematically studied the CRR activity of a series of DMSCs by means of density functional theory computations and micro-kinetics simulations. By using the adsorption strength of OH* and COOH* species as an indicator, three DMSCs, namely Cu/Mn, Ni/Mn and Ni/Fe, were identified as promising candidates after two-rounds of screening. Remarkably, it is found that the scaling relationship between the adsorption strength of COOH* and CO* species has been broken in these three DMSCs, leading to a superior CRR activity. Our work provides a useful guideline for further developing CRR electrocatalysts.