This　paper　proposes　a　decentralized　design　approach　of　optimal　consensus　protocols　of　the　multi-agent　system　(MAS)　via　the　directed-spanning-tree　(DST)-based　linear　transformation.　The　protocol　is　designed　by　using　DST-based　minimal　communication　links.　Firstly,　the　optimal　consensus　problem　of　MASs　is　transformed　into　the　optimal　control　problem　by　constructing　the　linear　transformation　based　on　a　DST　of　the　communication　topology.　Secondly,　a　new　distributed　protocol　is　designed　by　using　only　the　neighbor　information　on　the　DST　and　the　optimal　control　gain　is　obtained　by　using　the　linear　matrix　inequality　(LMI),　which　is　a　completely　decentralized　design　method.　Finally,　some　examples　are　given　to　verify　the　results.　©　2023　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.