In　this　paper　a　fast　algorithm　is　presented　for　numerically　solving　a　two-dimensional　fractional　mobile/immobile　convection-diffusion　model,　where　the　second-order　time　scheme　of　the　integer　derivative　and　the　L2-1　sigma　formula　of　the　time　Caputo　fractional　derivative　are　used　in　the　time　direction,　and　the　local　discontinuous　Galerkin　(LDG)　method　is　developed　to　approximate　the　space　direction.　The　stability　of　the　fully　discrete　LDG　scheme　is　proven,　and　the　a　priori　error　result　with　O(At2　+　hk+1　+　epsilon)　is　derived,　where　epsilon　is　the　tolerance　error.　Finally,　some　numerical　results　with　Qk(k　=　0,1,　2)　elements　are　given　to　verify　our　theoretical　results.