Evolution　equations　containing　fractional　derivatives　can　provide　suitable　mathematical　models　for　describing　anomalous　diffusion　and　transport　dynamics　in　complex　systems　that　cannot　be　modeled　accurately　by　normal　integer　order　equations.　Recently,　researchers　have　found　that　many　physical　processes　exhibit　fractional　order　behavior　that　varies　with　time　or　space.　The　continuum　of　order　in　the　fractional　calculus　allows　the　order　of　the　fractional　operator　to　be　considered　as　a　variable.　In　this　paper,　we　consider　the　mobile-immobile　advection-dispersion　model　with　the　Coimbra　variable　time　fractional　derivative　which　is　preferable　for　modeling　dynamical　systems　and　is　more　efficient　from　the　numerical　standpoint.　A　novel　implicit　numerical　method　for　the　equation　is　proposed　and　the　stability　of　the　approximation　is　investigated.　As　for　the　convergence　of　the　numerical　method,　we　only　consider　a　special　case,　i.e.,　the　time　fractional　derivative　is　independent　of　the　time　variable　t.　The　case　where　the　time　fractional　derivative　depends　on　both　the　time　variable　t　and　the　space　variable　x　will　be　considered　in　a　future　work.　Finally,　numerical　examples　are　provided　to　show　that　the　implicit　difference　approximation　is　computationally　efficient.　(C)　2013　Elsevier　Ltd.　All　rights　reserved.