The　purpose　of　this　paper　is　to　investigate　a　high　order　numerical　method　for　solving　time-fractional　Black-Scholes　equation　in　which　the　fractional　operator　is　defined　by　the　Caputo　fractional　derivative.　The　proposed　space-time　spectral　method　employs　the　Jacobi　polynomials　for　the　temporal　discretisation　and　Fourier-like　basis　functions　for　the　spatial　discretisation.　The　stability　and　convergence　of　the　numerical　scheme　are　analyzed.　Two　numerical　examples　are　considered　to　validate　the　accuracy　and　illustrate　the　practicability　of　the　proposed　method.　The　results　agree　with　the　theoretical　analysis　and　this　approach　can　be　applied　in　dealing　with　option　pricing　models　with　smooth　payoff　functions.　(C)　2021　IMACS.　Published　by　Elsevier　B.V.　All　rights　reserved.