Electrocatalytic nitrogen reduction reaction (e-NRR) is an attractive approach to produce NH3 because of the ambient conditions and abundant reactants. However, the catalytic performance of e-NRR catalysts is still insufficient, and far from replacing traditional method in NH3 synthesis. In this work, we study a series of Cu-based single-atom alloys, including 17 doped single transition metal (TM) atoms and 4 exposed surfaces with different Miller indices, through first-principles calculations, and finally identify five candidates (Re1-Cu(100), Re1-Cu(111), Os1-Cu(110), Os1-Cu(211), and W1-Cu(111)) with low limiting potential (-0.35 V, -0.38 V, -0.48 V, -0.49 V, and -0.42 V, respectively) as well as remarkable inhibition of the hydrogen evolution reaction for e-NRR. Our study indicates that the outstanding activity of the five candidates is caused by the strong coupling between the TM-d orbitals and the N2-2p orbitals. Furthermore, these catalysts also exhibit long-term stability. This work develops a universal strategy for the rapid screening and identification of highly efficient e-NRR catalysts.