Perfect　state　transfer　can　be　achieved　between　two　marked　vertices　of　graphs　like　a　star　graph,　a　complete　graph　with　self-loops　and　a　complete　bipartite　graph,　and　two-dimensional　Lattice　by　means　of　discrete-time　quantum　walk.　In　this　paper,　we　investigate　the　quality　of　quantum　state　transfer　between　two　marked　vertices　of　an　unsymmetrical　graph　like　the　butterfly　network.　Our　numerical　results　support　the　conjecture　that　the　fidelity　of　state　transfer　depends　on　the　quantum　state　to　be　transferred　dynamically.　The　butterfly　network　is　a　typical　example　studied　in　networking　coding.　Therefore,　these　results　can　provide　a　clue　to　the　construction　of　quantum　network　coding　schemes.