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
$\beta\in (1,2].$ 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.