Efficient and low-cost electrocatalysts are urgently required for the electrocatalytic N2 reduction reaction (NRR) to produce valuable NH3. Single-atom catalysts (SACs) represent one class of promising candidates. Besides the defects on the basal plane, very recently, the one-dimensional edge universally existing in the finite graphene or carbon sheet has gained attention as the anchoring site for SACs, which may enable unique catalytic mechanism. Herein, using first-principles calculations, we systematically investigated the NRR over SACs of transition metals (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Nb, Mo, and W) anchored by the N-modified edge of the graphene armchair nanoribbon (denoted as TM@GNR). Three criteria were employed to screen the best candidate from all the TM@GNR, including the high stability of TM@GNR, the preferable adsorption of N2 compared with H, and the lower applied potential for the first protonation of N2 compared with that of the active site. Accordingly, V(Nb)@GNR were theoretically demonstrated to be promising NRR electrocatalyst toward NH3 with low limiting potentials of -0.65 (-0.52) V, excellent selectivity of ∼100% (97%), and good stability. Particularly, NRR on the V@GNR and Nb@GNR precedes through a novel reaction mechanism with three spectator N2 molecules. Further analysis reveals that the strong capture and activation of N2 molecules by the edge-anchored V (Nb) atoms derives from their localized spin moment and atomic orbitals. Our studies emphasize the great potential of the edge of carbon materials to synthesize SACs for NRR and other reactions, and further reveal a novel NRR reaction mechanism on SACs.