In this paper, a new on-line inverse scattering methodology, which is based on radial basis function neural networks, is presented. The construction of these networks is implemented by means of the orthogonal least squares algorithm. By applying this training algorithm we can calculate the values of the free parameters of the network and also define its structure. Thus a trial-and-error strategy concerning the definition of the network size is avoided. In particular, the network is constructed to perform the mapping from scattered-field measurements to electromagnetic and geometric properties of the scatterer. Although this approach can be applied to various inverse scattering applications, we focus on the reconstruction of cylindrical dielectric scatterers from simulated measurements of the scattered electric field, while transverse magnetic illuminations are used. The objective is to estimate the relative dielectric constant, the size, and the position of the scatterer. In numerical results an investigation of the performance of the network is carried out. After the completion of the training procedure the network can rapidly estimate the scatterer properties, without extreme storage demands. Finally, the robustness of the proposed methodology in inverting measurements that are corrupted by additive white Gaussian noise is examined.