The numerical solution of the time fractional Black–Scholes model (TFBSM) of order 0 < α < 1 governing European options is studied. Zhang et al. (2016) derived a numerical scheme of second-order in space. We improve their results by constructing a scheme of fourth-order in space while keeping 2−α in time. The solvability, stability and convergence of the proposed numerical scheme are proved using a Fourier analysis. The results are demonstrated on two examples.