At present, nitrogen reduction reaction (NRR) has become one critical method for NH3 production through the single-atom catalyst (SAC). A variety of TM@β-Te SACs, constructed by 28 transition metal (TM) atoms anchoring on monovacant β-Te substrate, are systematically investigated by using DFT calculations. An efficient "six-step" screening scheme is proposed to screen out potential NRR catalysts, during which the implicit and explicit solvent models are involved to evaluate competitive reactions of H2O and H+. The final selected (Ta, W)@β-Te catalysts have limiting potentials (UL) of −0.32 V and −0.37 V, respectively. Three intrinsic descriptors of φ (the ratio of number of valence electrons and electronegativity of TM atom), ΔG∗N(adsorption energy of a single N atom on the substrate) and ICOHP (Crystal orbital Hamiltonian integrals for TM-N bonds) are proposed and their correlations with UL are investigated to expound the catalytic activity and mechanism. The relationships of dN≡N ∼ φ, ΔG∗N2∼ φ, ΔG∗N∼ φ and ICOHP ∼ φ resemble "volcanoes", where (Ta, W)@β-Te are located near the vertex as potential catalysts, which can be verified by scaling relationship of ICOHP and ΔG∗N. Moreover, the UL ∼ φ, UL ∼ ΔG∗Nand UL ∼ ICOHP can be used to determine the potential catalysts from rough catalyst screening to accurate determination of potential determining step (PDS) in catalytic reaction. The constant potential model is adopted to investigate the influences of electrode potentials on adsorption strength of NRR intermediates. This work is informative for the research of NRR process and catalyst design of monoalkenes, which offers an efficient and dependable approach for screening excellent NRR catalysts and revealing the origin of catalytic activity.