The　aim　of　this　paper　is　to　investigate　the　boundary　value　problem　of　a　fractional　q-difference　equation　with　phi-Laplacian,　where　phi-Laplacian　is　a　generalized　p-Laplacian　operator.　We　obtain　the　existence　and　nonexistence　of　positive　solutions　in　terms　of　different　eigenvalue　intervals　for　this　problem　by　means　of　the　Green　function　and　Guo-Krasnoselskii　fixed　point　theorem　on　cones.　Finally,　we　give　some　examples　to　illustrate　the　use　of　our　results.