The highly selective and active nitrate-to-ammonia electrochemical conversion (NO3 reduction reaction [NO3RR]) can be an appealing and supplementary alternative to the Haber-Bosch process. It also opens up a new idea for addressing nitrate pollution. Previous study demonstrated that FeN4 single-atom catalyst (SAC) indicates excellent NO3RR performance. Nonetheless, the mechanism that triggers the electrocatalytic NO3RR remains unclear. The feasibility of NO3RR over various SACs is verified in this study via high-throughput density functional theory calculations with the single transition metal (TM) atom coordinated with four nitrogen atoms supported on graphene as the example. We conducted a comprehensive screening of TM SAC candidates for stability, NO3− adsorption strength, catalytic activity, and selectivity. Results reveal that the most promising candidate among the 23 TM SACs is Os SAC with a low limiting potential of −0.42 V. Os SAC is better than Fe SAC with a limiting potential of −0.53 V because of the strong interaction between the oxygen of NO3− species and Os atom. The origin of high NO3RR activity of Os SAC is explained by its inner electronic structure of the strong hybridization of the Os atom and NO3− caused by the increasing charge transfer from TM atom to NO3−, leading to the suitable NO3− adsorption. This research provides a fundamental insight of discovering novel NO3RR catalysts and may provide a motivating drive for the creation of effective ammonia electrocatalysts for further experimental investigation.