The catalytic performance of a series of single transition metal (TM = 3d, 4d, and 5d series) atoms anchored on B/N co-doped graphene (BxNy@Gra) toward electrocatalytic nitrogen reduction reaction (eNRR) was systematically investigated by first-principles calculations. Among 180 possible materials, four catalysts (Tc-B1N3@Gra, Os-B2N2α@Gra, Re-B2N2γ@Gra, Nb-B3N1@Gra) feature the highest activity with UL no higher than 0.31 V. Interestingly, a volcano curve between UL and ΔEads(*NNH) can be established, so ΔEads(*NNH) can be applied as a descriptor to unveil the structure-activity relationship and characterize the activity of catalysts. The properties, thermal stability, and selectivity for the four catalysts were analyzed. Os-B2N2α@Gra is identified as a promising catalyst in this work for catalyzing N2 electroreduction to NH3 owing to its potent catalytic activity (UL = −0.28 V), high stability and distinct selectivity. This work can give some meaningful guidance for rapid screening and the rational design of efficient single-atom catalysts for electrocatalytic ammonia synthesis and other related electrochemical reaction. We expect that the present study will inspire and promote the efforts from both experimental and theoretical in this direction.