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In this paper, we develop a new approximation technique for solving space fractional diffusion equation. The method of solution is based on fractional order Legendre function with the concept of Caputo’s definition of fractional derivatives. Convergence analysis and error bound of the method are discussed. Several Illustrative examples are included to demonstrate the validity and applicability of the proposed method. The obtained results reveal that the method is more accurate and efficient than the methods such as Chebyshev finite difference method and Tau approach method discussed in the literature. Keywords: Fractional order Legendre function, Caputo’s fractional derivative, Space fractional diffusion equation, Convergence analysis, Error estimation