Quantum　information　and　quantum　computation　have　achieved　a　huge　success　during　the　last　years.　In　this　paper,　we　investigate　the　capability　of　quantum　Hash　function,　which　can　be　constructed　by　subtly　modifying　quantum　walks,　a　famous　quantum　computation　model.　It　is　found　that　quantum　Hash　function　can　act　as　a　hash　function　for　the　privacy　amplification　process　of　quantum　key　distribution　systems　with　higher　security.　As　a　byproduct,　quantum　Hash　function　can　also　be　used　for　pseudorandom　number　generation　due　to　its　inherent　chaotic　dynamics.　Further　we　discuss　the　application　of　quantum　Hash　function　to　image　encryption　and　propose　a　novel　image　encryption　algorithm.　Numerical　simulations　and　performance　comparisons　show　that　quantum　Hash　function　is　eligible　for　privacy　amplification　in　quantum　key　distribution,　pseudo-random　number　generation　and　image　encryption　in　terms　of　various　hash　tests　and　randomness　tests.　It　extends　the　scope　of　application　of　quantum　computation　and　quantum　information.