Q-calculus　plays　an　extremely　important　role　in　mathematics　and　physics,　especially　in　quantum　physics,　spectral　analysis　and　dynamical　systems.　In　recent　years,　many　scholars　are　committed　to　the　research　of　nonlinear　quantum　difference　equations.　However,　there　are　few　works　about　the　nonlinear　q-difference　equations　with　p-Laplacian.　In　this　paper,　we　investigate　the　solvability　for　nonlinear　second-order　quantum　difference　equation　boundary　value　problem　with　one-dimensional　p-Laplacian　via　the　Leray-Schauder　nonlinear　alternative　and　some　standard　fixed　point　theorems.　The　obtained　theorems　are　well　illustrated　with　the　aid　of　two　examples.