When　considering　the　price　change　of　the　underlying　fractal　transmission　system,　a　fractional　Black-Scholes(B-S)　model　with　an　α-order　time　fractional　derivative　is　derived.　In　this　paper,　we　discuss　the　numerical　simulation　of　this　time　fractional　Black-Scholes　model　(TFBSM)　governing　European　options.　A　discrete　implicit　numerical　scheme　with　a　spatially　second-order　accuracy　and　a　temporally　2-α　order　accuracy　is　constructed.　Then,　the　stability　and　convergence　of　the　proposed　numerical　scheme　are　analyzed　using　Fourier　analysis.　Some　numerical　examples　are　chosen　in　order　to　demonstrate　the　accuracy　and　effectiveness　of　the　proposed　method.　Finally,　as　an　application,　we　use　the　TFBSM　and　the　above　numerical　technique　to　price　several　different　European　options.　©　2016　Elsevier　Ltd.　All　rights　reserved.