<p>In this paper, we consider preconditioning the structured linear systems arising from the numerical solution of time-dependent two-sided space-fractional diffusion equations (TSFDE) problems with variable coefficients. The coefficient matrices possess the structure of the sum of the identity matrix and multiplications of diagonal matrices and Toeplitz matrices. We propose a structured preconditioning method based on the separation of matrices and approximations of the involved Toeplitz matrices. The proposed method provides a good approximation to the original matrix and fast algorithms can be used to compute matrix-vector products involving the inverse. Spectral properties of the preconditioned matrices are analyzed and bounds of the condition number are provided. Numerical results demonstrate that the proposed preconditioner achieves superior computational efficiency and stability.</p>