In　this　paper,　a　second　order　accurate　time　and　space　difference　method　is　proposed　to　solve　the　nonlinear　two-sided　space-fractional　diffusion　equation　with　variable　coefficients.　We　combine　the　alternating　direction　implicit　method　and　Bi-conjugate　gradient　stabilized　iterative　solver　to　develop　an　efficient　numerical　method　for　a　two　dimensional,　nonlinear,　two-sided　space-fractional　diffusion　equation　with　variable　coefficients.　Furthermore,　the　proposed　method　is　proved　to　be　uniquely　solvable,　stable　and　convergent.　Finally,　some　numerical　results　verify　the　accuracy　and　efficiency　of　our　computational　approach.　©　2020　IMACS