A kind of multiple-time two-sided space fractional advection-diffusion equation is considered. Based on the shifted Grünwald-Letnikov formula, the spatial fractional order derivatives in the equations are approximated by the weighted average finite difference method, energy estimation is used, mathematical induction and numerical examples are used to illustrate the reliability and validity of the proposed difference format. A weighted implicit finite difference format, the stability of the difference format, and the convergence of the difference format are achieved. By comparing the numerical and exact solutions of the example equation, the theoretical results are verified.