In this thesis, two dimensional two-sided space fractional diffusion equations with variable diffusion coefficients are discussed. The problems can be solved by an implicit finite difference scheme, which is proven to be uniquely solvable, unconditionally stable and first-order convergent in infinity norm. Nonsingular block circulant with circulant block preconditioners are proposed to accelerate the convergence rate of the Krylov subspace linear system solver efficiently. The preconditoned matrix equals to a sum of the identity matrix, a matrix with small norm and a matrix with low rank under certain conditions, so that a fast convergence is obtained. Moreover, the preconditioners are practical with both an operation cost of O(N log N) and an O(N) memory. Numerical examples are also given.