Metallic Cu is a well-known electrocatalyst for nitrate reduction reaction (NO3RR), but it suffers from relatively low activity, poor stability, and inducing nitrite accumulation during the long-term operation. Herein, it is found that Cu catalysts minimized at the single-atom level can overcome the limitations of bulk materials in NO3RR. A metal-nitrogen-carbon (M-N-C) electrocatalyst composed of carbon nanosheets embedding isolated copper atoms coordinated with N, Cu-N-C-800, is synthesized by pyrolysis of a Cu-based metal-organic framework at 800 degrees C. In comparison with Cu nanoparticles and Cu plate-800, kinetic measurements show that the Cu-N-C-800 electrocatalyst is more active and stable and distinctly suppresses the release of nitrite intermediate into the solution. The combined results of experimental data and density functional theory calculations indicate that Cu bound with N (particularly Cu-N-2) is the key to favorable adsorption of NO3- and NO2-. This strong binding is responsible for the enhanced rate of nitrate conversion to the end products of ammonia and nitrogen. These findings highlight the promise of single-atom Cu electrocatalysts for nitrate reduction with desirable performance.