<p>Fractional advection-dispersion equations (ADEs) have become a promising alternative to interpret the anomalous solute transport of fluid flow in heterogeneous porous media, but the numerical study of high-dimensional space-fractional ADEs on irregular domains remains a challenging task. This research aims to establish an efficient local radial basis function (RBF) meshfree method for the space-fractional ADEs on three-dimensional irregular convex domains. We discretize the fractional derivative at a given node via a weighted linear sum of the functional values on scattered node layouts by using its linearity and determine the weights in a finite-sized neighborhood around this node. The proposed method overcomes the drawback of ill-conditioning issue while simultaneously providing high efficiency and the ease of implementation. It can be applied on a set of arbitrarily distributed nodes without any underlying mesh to connect them, thereby showing great geometric flexibility to irregular domains. The capability and computational accuracy are authenticated by the benchmark tests over some convex domains.</p>