Structure engineering represents a powerful strategy for fine tuning the catalytic activity of catalysts. However, correlating the structural properties with catalytic performance is challenging because it is difficult to characterize the surface structure of catalysts, which restricts the use of structure engineering as a tool to optimize the catalytic performance. Herein, we demonstrate the effects of structural properties (e.g., the coordination number and strain) in CO2 reduction reaction (CRR) by focusing on icosahedral, octahedral and cuboctahedral Cu nanoparticles with the diameters from 1.5 to 2.5 nm by density functional theory calculations. A series of linear relations between the binding energy of CRR intermediates and generalized coordination number (GCN) or surface strain are established. We proposed that GCN and strain can be used as the predictive descriptors correlating the structural properties of Cu-based catalysts to its catalytic performance in CRR. By coupling of GCN and strain effects, we predicted that the octahedral Au@Cu core shell nanoparticle could lower the overpotentials to convert CO2 into CH4. We hoped that the presented structure-activity relations will provide useful insight for the design better Cu-based catalysts for CRR by structure engineering. (C) 2019 Elsevier Inc. All rights reserved.