In　this　paper,　we　consider　the　numerical　solution　of　the　fractional　Cable　equation,　which　is　a　generalization　of　the　classical　Cable　equation　by　taking　into　account　the　anomalous　diffusion　in　the　movement　of　the　ions　in　neuronal　system.　A　schema　combining　a　finite　difference　approach　in　the　time　direction　and　a　spectral　method　in　the　space　direction　is　proposed　and　analyzed.　The　main　contribution　of　this　work　is　threefold:　1)　We　construct　a　finite　difference/Legendre　spectral　schema　for　discretization　of　the　fractional　Cable　equation.　2)　We　give　a　detailed　analysis　of　the　proposed　schema　by　providing　some　stability　and　error　estimates.　Based　on　this　analysis,　the　convergence　of　the　method　is　rigourously　established.　We　prove　that　the　overall　schema　is　unconditionally　stable,　and　the　numerical　solution　converges　to　the　exact　one　with　order　O(4t2-max{a,ß}),　where　4t　is　the　time　step　size,　a　and　ß　are　two　different　exponents　between　0　and　1　involved　in　the　fractional　derivatives.　3)　Finally,　some　numerical　experiments　are　carried　out　to　support　the　theoretical　claims.　©　MODSIM　2009.All　rights　reserved.