The main purpose of this paper is to examine the effectiveness of Half-Sweep Gauss-Seidel (HSGS) method for Space-Fractional diffusion equations. The Caputo's derivative and implicit finite difference scheme will be used to discretize linear space-fractional equation of the first order to construct system linear equation. The basic formulation and application of the HSGS iterative method are also presented. Two numerical examples and comparison with other iterative methods shows that the present method is effective. Based on computational numerical result, the solution obtained by proposed iterative method is in excellent agreement, it can be concluded that the proposed iterative method is superior to the Full-Sweep Gauss-Seidel (FSGS) iterative method