Hash　functions　play　an　essential　role　in　many　cryptographic　applications　such　as　digital　signature,　integrity　authentication,　and　key　derivation.　Most　of　them　are　iteratively　built　based　on　the　Merkle-Damgard　(MD)　structure.　Unfortunately　the　traditional　MD　structure　is　suffering　from　various　attacks,　and　thus　the　design　of　new　hash　functions　is　emerging.　In　this　paper,　inspired　by　quantum　computation,　we　present　a　new　hash　function　by　introducing　alternate　single-qubit　coin　operators　into　discrete-time　quantum　walk.　The　present　hash　function　is　classical　with　classical　input　and　output.　The　compressive　function　can　be　implemented　by　performing　alternate　single-qubit　coin　operators　on　the　coin　state　controlled　by　a　classical　input　binary　message　and　then　applying　the　global　conditional　shift　operator　on　the　position　state　and　the　coin　state.　The　classical　output　hash　value　is　generated　by　making　amplification,　truncation,　and　modular　operation　on　the　final　probability　distribution.　Numerical　simulation　and　performance　comparison　show　that　the　present　hash　function　has　an　excellent　property　of　collision　resistance　and　easier　implementation　than　existing　quantum-walk-based　hash　functions.　It　promotes　more　applications　of　quantum　computation　in　the　design　of　hash　functions.