To　grasp　the　target　object　stably　and　orderly　in　the　object-stacking　scenes,　it　is　important　for　the　robot　to　reason　the　relationships　between　objects　and　obtain　intelligent　manipulation　order　for　more　advanced　interaction　between　the　robot　and　the　environment.　This　paper　proposes　a　novel　graph-based　visual　manipulation　relationship　reasoning　network　(GVMRN)　that　directly　outputs　object　relationships　and　manipulation　order.　The　GVMRN　model　first　extracts　features　and　detects　objects　from　RGB　images,　and　then　adopts　graph　convolutional　network　(GCN)　to　collect　contextual　information　between　objects.　To　improve　the　efficiency　of　relation　reasoning,　a　relationship　filtering　network　is　built　to　reduce　object　pairs　before　reasoning.　The　experiments　on　the　Visual　Manipulation　Relationship　Dataset　(VMRD)　show　that　our　model　significantly　outperforms　previous　methods　on　reasoning　object　relationships　in　object-stacking　scenes.　The　GVMRN　model　is　also　tested　on　the　images　we　collected　and　applied　on　the　robot　grasping　platform.　The　results　demonstrated　the　generalization　and　applicability　of　our　method　in　real　environment.