Nowadays,　many　researches　have　considerable　attention　to　the　nonlinear　q-difference　equations　boundary　value　problems　as　important　and　useful　tool　for　modeling　of　different　phenomena　in　various　research　fields.　In　this　work,　we　investigate　a　class　of　q-difference　equations　boundary　value　problems　with　integral　boundary　conditions　with　p-Laplacian　on　infinite　intervals.　By　applying　the　Avery-Peterson　fixed　point　theorem　in　a　cone,　we　establish　the　existence　of　three　positive　solutions　for　the　above　boundary　value　problem.　Finally,　the　main　results　is　illustrated　with　the　aid　of　an　example.