Iron　and　nitrogen　co-doped　carbons　(Fe-N-C)　have　comparable　activity　to　Pt-based　catalysts　for　oxygen　reduction　reaction　(ORR),　but　with　much　poorer　durability　in　acidic　electrolytes.　Recently,　regulating　the　coordination　environment　of　Fe　center　(in-plane　or　axially)　to　boost　the　ORR　activity　of　Fe-N-C　has　attracted　many　interests,　and　the　axial　OH　ligand　is　even　regarded　as　a　necessary　part　of　a　highly-active　structure.　However,　the　influence　of　these　regulations　on　the　stability　is　still　not　clear.　Herein,　we　performed　kinetic　and　thermodynamic　calculations　based　on　density　functional　theory　with　explicit　consideration　of　electrode　potential　to　study　the　OH　axial　ligand　effect　on　the　stability　of　Fe-N-C　electrocatalysts.　We　found　that　although　the　OH　ligand　can　enhance　the　ORR　onset　potential　to　some　extent,　it　substantially　increases　the　H2O2　selectivity,　pushing　ORR　diverted　to　the　2e+　2e-pathway.　In　the　latter　2e-process　(H2O2　reduction),　harmful　hydroxyl　radicals　could　be　produced　upon　H2O2　dissociation.　Therefore,　from　the　perspective　of　catalysts＇　stability,　OH　ligand　coordination　on　the　metal　center　is　not　a　good　way　to　develop　stable　ORR　catalysts.