Designing efficient nitrogen reduction reaction (NRR) electrocatalysts for ammonia (NH3) synthesis under mild conditions is an attracting and challenging theme in energy electrocatalysis. Herein, the catalytic activity of a series of 3d (Cr, Mn, Fe, Co, Ni), 4d (Mo, Tc, Ru, Rh, Pd) and 5d (W, Re, Os, Ir, Pt) transition-metal (TM) atoms anchored Janus MoSSe monolayers for NRR is systematically explored by means of the first-principles calculations. A four-step NRR screening strategy (Delta G(*N-2) < 0 eV, Delta G(*N-2 -> *NNH) < 0.50 eV, Delta G(*NH2 -> *NH3) < 0.50 eV and Delta G(*N-2) < Delta G(*H)) is designed and applied to 15 TM-MoSSe systems, and only the Mo-, Re- and OsMoSSe stand out. The reaction mechanisms of NRR on Mo-, Re- and Os-MoSSe are all via the distal pathway and exhibit excellent catalytic activity (with the limiting potentials of -0.49, -0.39 and -0.49 V, respectively), especially the Re-MoSSe. The high NRR activity of the Mo-, Re- and Os-MoSSe can originate mainly from the effective activation of N-2, high built-in electrical field and superior electrical conductivity. Present findings may suggest a reliable and effective NRR screening strategy for the design of NRR electrocatalysts and promote the further exploration and development of novel NRR electrocatalysts.