Ammonia is an important chemical in both industry and agriculture. The production of ammonia in a green way is challenging. The electrochemical nitrogen reduction reaction (e-NRR) has been proposed for this purpose. However, this technology is still far from practical applications due to low production, which is mainly because of inefficient electrocatalysts. In this work, we have designed a series of single-atom catalysts (SACs) anchored on waved graphene (wG) for efficient e-NRR and systematically investigated the effect of curvature on the catalytic performance based on first-principles calculations. Eight SACs (V, Cr, Mn, Fe, Co, Ni, Cu, and Pt) anchored on waved graphene with various curvatures (0-50%) have been studied. We found that the curvature strongly affected the formation, catalytic activity, and selectivity of SACs for e-NRR: (1) the formation possibility of SACs on wG was considerably enhanced on increasing the curvature. (2) The free energies for the rate-determining steps of SAC-V-wG, SAC-Mn-wG, and SAC-Cr-wG were less than 1.0 eV, leading to high catalytic activity for e-NRR. In particular, SAC-Mn-wG exhibited higher activity for e-NRR than SAC-Mn on flat graphene. (3) The three systems had higher selectivity for e-NRR than for HER, which could be further improved by compression. Thus, we conclude that SAC-Mn-wG is the best SAC on wG for e-NRR because of its easy fabrication, good catalytic performance and high selectivity. We believe that our findings can provide new insights in reported experimental results and guidance for the design of novel SACs with high performance for e-NRR.