This paper presents an alternating direction implicit (ADI) scheme specifically designed for the two-dimensional space-fractional diffusion equation, utilizing a spatially nonuniform mesh that effectively addresses boundary singularities. The nonlocal operator of the fractional derivatives leads to dense and ill-conditioned linear systems, particularly in high-dimensional cases. The ADI scheme transforms the high-dimensional problem into a series of one-dimensional problems, significantly reducing the size of the linear system. We establish the stability of the ADI scheme through a thorough analysis of the spectral properties of the coefficient matrix. To further enhance efficiency, we introduce a banded preconditioner with diagonal compensation, which improves the spectrum of the coefficient matrices and accelerates the convergence rate of the Krylov subspace method. Numerical experiments demonstrate both the accuracy of the ADI scheme and the improved computational efficiency achieved with the banded preconditioner.