A Riesz space-fractional reaction-dispersion equation (RSFRDE) is obtained from the classical reaction-dispersion equation (RDE) by replacing the second-order space derivative with a Riesz derivative of order β ∈ (1, 2]. In this paper, using Laplace and Fourier transforms, we obtain the fundamental solution for a RSFRDE. We propose an explicit finite-difference approximation for a RSFRDE in a bounded spatial domain, and analyse its stability and convergence. Some numerical examples are presented.2000 Mathematics subject classification: primary 60J60; secondary 60J15, 60G52, 26A33, 65M12, 65M06.