In this paper, we propose a numerical scheme to solve space fractional order diffusion equation. Our scheme uses shifted Chebyshev polynomials of the third kind. The fractional differential derivatives are expressed in terms of the Caputo sense. Moreover, Chebyshev collocation method together with the finite difference method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical approximations performed by the proposed method are presented and compared with the results obtained by other numerical methods. The results reveal that our method is a simple and effective numerical method