We　study　the　problem　of　quantum　multi-unicast　communication　over　the　butterfly　network　in　a　quantum-walk　architecture,　where　multiple　arbitrary　single-qubit　states　are　transmitted　simultaneously　between　multiple　source-sink　pairs.　Here,　by　introducing　quantum　walks,　we　demonstrate　a　quantum　multiunicast　communication　scheme　over　the　butterfly　network　and　the　inverted　crown　network,　respectively,　where　the　arbitrary　single-qubit　states　can　be　efficiently　transferred　with　both　the　probability　and　the　state　fidelity　one.　The　presented　result　concerns　only　the　butterfly　network　and　the　inverted　crown　network,　but　our　techniques　can　be　applied　to　a　more　general　graph.　It　paves　a　way　to　combine　quantum　computation　and　quantum　network　communication.