In this paper, we obtain the solution of a time-space fractional dif-fusion equation by integral transform method. The method of integral transform based on using a fractional generalization of the Fourier trans-form and the classical Laplace transform. The solution is derived in a closed and computational form in terms of the Mittag-Leffler function.It provides an elegant extension of a result given earlier by Nikolova and Boyadjiev [20].