In this paper, we introduce a new semi-analytical method called the homotopy analysis Shehu transform method (HASTM) for solving multidimensional fractional diffusion equations. The proposed technique is a combination of the homotopy analysis method and the Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms. Shehu transform is user-friendly, and its visualization is easier than the Sumudu, and the natural transforms. The convergence analysis of the method is proved, and we provide some applications of the fractional diffusion equations to validate the efficiency and the high accuracy of the technique. The results obtained using the HASTM are in complete agreement with the results of the existing techniques.