Production　of　ammonia　(NH3)　by　electrocatalytic　reduction　of　nitrate　(NO3RR)　not　only　eliminates　harmful　pollution,　but　also　provides　a　way　to　reduce　the　energy　consumption　associated　with　predominated　Haber-Bosch　process.　However,　realization　of　this　process　still　faces　many　challenges　because　of　the　complexity　of　the　reaction　mechanism.　Here　we　investigated　the　catalytic　activity　and　selectivity　of　a　series　of　graphdiyne　supported　single　atom　catalysts　(SACs),　namely　TM/GDY,　for　the　reduction　of　NO3-　to　NH3　by　first-principles　calculations.　Among　the　10　SACs　studied,　Fe/GDY　was　found　to　have　good　catalytic　performance,　consistent　with　the　fact　that　the　Fe-doped　GDY　molecular　layer　was　located　near　the　top　of　the　volcano　plot,　with　a　reaction　limit　potential　of　-0.44　V　and　showed　excellent　selectivity　in　inhibiting　the　competitive　hydrogen　evolution　reaction　(HER).　The　formation　of　the　by-products　NO2,　NO,　N2O　and　N-2　on　Fe/GDY　requires　a　considerable　energy　barrier,　which　ensures　high　selectivity.　Furthermore,　detailed　electronic　property　analyses　indicate　that　the　GDY　can　work　as　an　electron　repository　to　effectively　balance　the　charge　transfers　during　the　reaction　process.　This　study　not　only　offers　an　eligible　NO3RR　electrocatalyst　but　also　provides　an　atomic　understanding　of　the　mechanisms　of　the　NO3RR　process　behind.