Electrochemical　production　of　hydrogen　peroxide　(H2O2)　is　a　sustainable　and　environmentally　benign　process.　The　electrochemical　oxygen　reduction　process　(ORR)　via　a　two　electron　pathway　(2e-　ORR)　offers　a　practical　method　for　on-site　H2O2　generation.　As　an　earth-abundant　catalyst,　the　cobalt-nitrogen　coordinated　systems　integrated　into　the　carbon　matrix　(Co-NC)　has　caused　wide　attention　for　its　high　activity　in　2e-　ORR.　Even　though　most　of　the　reported　Co-NC　catalysts　have　classical　planar　Co-N4　coordination,　axial　coordination　engineering　has　recently　emerged　as　an　effective　way　to　control　the　active　sites　in　the　axial　direction　by　using　different　coordination　ligands.　The　structure-function　link　between　the　Co-N　configuration　of　non-planar　coordination　and　2e-　ORR　activity　is,　however,　not　fully　understood.　An　axial-N　coordinated　Co-N5　motif　embedded　in　hierarchically　porous　graphite-3R　carbon　(Co-N5C)　was　effectively　synthesized　using　a　template-sacrificing　method.　The　Co-N5C　has　a　high　selectivity　for　2e-　ORR　and　a　high　H2O2　molar　production　rate　of　up　to　6.78　mol　peroxide/　gcatalyst/h　in　acidic　media,　both　of　which　are　better　than　its　Co-N4　counterpart.　DFT　analyses　demonstrate　that　axial-N　ligands　regulated　the　d-band　center　of　the　Co　atom　in　the　Co-N5C　catalyst,　inducing　a　shift　in　&　UDelta;G*OOH　near　the　Sabatier　volcano　plot＇s　peak　(&　UDelta;G*OOH　=　4.22　eV).　This　optimized　the　binding　of　the　*OOH　intermediate　and　then　enhanced　the　protonation　of　*OOH　to　produce　H2O2　more　efficiently.