The raindrop size distribution (RSD) is a critical factor in estimating rain intensity using advanced dual-polarized weather radars. A new neural-network algorithm to estimate the RSD from S-band dual-polarized radar measurements is presented. The corresponding rain rates are then computed assuming a commonly used raindrop diameter speed relationship. Numerical simulations are used to investigate the efficiency and accuracy of this method. A stochastic model based on disdrometer measurements is used to generate realistic range profiles of the RSD parameters, while a T-matrix solution technique is adopted to compute the corresponding polarimetric variables. The error analysis, which is performed in order to evaluate the expected errors of this method, shows an improvement with respect to other methodologies described in the literature. A further sensitivity evaluation shows that the proposed technique performs fairly well even for low specific differential phase-shift values