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In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β∈(1, 2].We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are analyzed. Numerical results are found in good agreement with the theoretical analysis.