This　paper　studies　the　distributed　consensus　problem　of　general　linear　multi-agent　systems　(MASs)　based　on　a　novel　decentralized　output　feedback　control　approach.　By　introducing　the　edge　state　and　a　directed-spanning-tree-based　linear　transformation　method,　we　firstly　equivalently　transform　the　consensus　problem　into　the　decentralized　output　feedback　stabilization　control　problem.　Then　we　employ　the　properties　of　distributed　fixed　modes　in　decentralized　output　feedback　stabilization　control　problem　to　derive　a　necessary　and　sufficient　condition　for　ensuring　the　asymptotic　state　consensus　of　the　MAS　under　the　linear　state　feedback　control.　We　further　present　a　gradient　descent　iterative　algorithm　to　design　the　gain　matrix　in　the　linear　feedback　consensus　protocol.　Finally,　we　give　a　numerical　example　to　demonstrate　the　effectiveness　of　the　theoretical　results.