Two-dimensional carbon materials and their derivatives are widely applied as promising electrocatalysts and supports of single-atom sites. Theoretical investigations of 2D carbon materials are usually based on planar models, yet ignore local curvature brought on by possible surface distortion, which can be significant to the exact catalytic performance as has been realized in latest research. In this work, the curvature-influenced electrocatalytic nitrogen reduction reaction (NRR) reactivity of heme-like FeN₄ single-atom site was predicted by a first-principle study, with FeN₄-CNT(m,m) (m = 5~10) models adopted as local curvature models. The results showed that a larger local curvature is favored for NRR, with a lower limiting potential and higher N₂ adsorption affinity, while a smaller local curvature shows lower NH₃ desorption energy and is beneficial for catalyst recovery. Using electronic structures and logarithm fitting, we also found that FeN₄-CNT(5,5) shows an intermediate-spin state, which is different from the high-spin state exhibited by other FeN₄-CNT(m,m) (m = 6~10) models with a smaller local curvature.