In　recent　years,　graph　neural　network　has　become　the　main　paradigm　for　solving　graph　analysis　tasks,　which　can　easily　process　high-dimensional　data　and　has　a　powerful　fitting　capability.　Recent　works　on　graph　neural　networks　have　successfully　transferred　the　convolution　network　in　computer　vision　to　graph.　Graph　convolution　network　(GCN)　has　become　the　classical　network　framework　in　graph　neural　networks　due　to　its　simple　aggregation　approach　and　favorable　theoretical　support.　When　the　original　graph　data　are　constructed,　an　adjacency　matrix　is　used　to　represent　the　topology,　where　0　or　1　indicates　whether　there　is　a　connection　between　nodes.　Moreover,　GCN　aggregates　node　attributes　only　depends　on　adjacency　matrix.　Although　it　can　learn　a　mapping　function,　its　message　propagation　mechanism　is　fixed　for　a　given　adjacency　matrix.　However,　for　specific　downstream　tasks,　we　expect　to　propagate　messages　relevant　to　the　downstream　task,　while　a　fixed　aggregation　mode　cannot　handle　this.　To　this　end,　we　propose　a　graph　convolution　neural　network　with　a　learnable　message　propagation　mechanism.　The　original　adjacency　matrix　is　adjusted　through　a　learnable　weight,　so　that　the　message　propagation　mechanism　better　adapts　to　downstream　tasks.　Experimental　results　show　that　the　proposed　model　achieves　significant　performance　in　node　classification.　©　2023　IEEE.