Heterogeneous　graph　neural　networks　play　a　crucial　role　in　discovering　discriminative　node　embeddings　and　relations　from　multi　-relational　networks.　One　of　the　key　challenges　in　heterogeneous　graph　learning　lies　in　designing　learnable　meta　-paths,　which　significantly　impact　the　quality　of　learned　embeddings.　In　this　paper,　we　propose　an　Attributed　Multi　-Order　Graph　Convolutional　Network　(AMOGCN),　which　automatically　explores　meta　-paths　that　involve　multi　-hop　neighbors　by　aggregating　multi　-order　adjacency　matrices.　The　proposed　model　first　constructs　different　orders　of　adjacency　matrices　from　manually　designed　node　connections.　Next,　AMOGCN　fuses　these　various　orders　of　adjacency　matrices　to　create　an　intact　multi　-order　adjacency　matrix.　This　process　is　supervised　by　the　node　semantic　information,　which　is　extracted　from　the　node　homophily　evaluated　by　attributes.　Eventually,　we　employ　a　one　-layer　simplifying　graph　convolutional　network　with　the　learned　multi　-order　adjacency　matrix,　which　is　equivalent　to　the　cross　-hop　node　information　propagation　with　multilayer　graph　neural　networks.　Substantial　experiments　reveal　that　AMOGCN　achieves　superior　semi　-supervised　classification　performance　compared　with　state-of-the-art　competitors.