On-line monitoring of power system voltage security has become a very demanding task in competitive power market operation and fast estimation of bus voltage is essential for this. In this paper, a novel parallel radial basis function neural network (PRBFN) which is a multistage network, in which stages operate in parallel rather than in series during testing, has been developed to predict bus voltage magnitudes in an efficient manner. The non-linear mapping capability of radial basis function has been exploited along with forward-backward training. Entropy concept has been used to select the input features of PRBFN to reduce the size of the neural network. The proposed method using a single PRBFN is used to estimate bus voltages under different topological and operating conditions of IEEE 30-bus and a practical 75-bus Indian system