The　hash　function　is　an　important　branch　of　cryptology.　The　controlled　quantum　walk-based　hash　function,　which　is　presented　by　Li,　is　a　kind　of　novel　hash　function.　It　is　safe,　flexible,　and　compatible.　All　existing　controlled　quantum　walk-based　hash　functions　are　controlled　by　one　bit　of　message　in　each　step.　To　process　the　message　in　batch　amounts,　in　this　paper,　the　controlled　alternate　quantum　walk-based　block　hash　function　is　presented　by　using　the　time-position-dependent　controlled　alternate　quantum　walk　on　the　complete　graph　with　self-loops.　The　presented　hash　function　accelerates　the　hash　processing　dramatically,　so　it　is　more　efficient.　That　could　save　many　resources　and　execution　time　further.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.