Abstract Fast estimation of bus voltage magnitude is essential for security monitoring and analysis of power system. An approach based on a parallel self-organising hierarchical neural network (PSHNN) is proposed to estimate bus voltage magnitudes at all the PQ buses of a power system in an efficient manner. PSHNN is a multi-stage neural network in which stages operate in parallel rather than in series during testing. The revised back-propagation algorithm is used for learning input non-linearities along with forward-backward training of stage neural networks. A method based on Euclidean distance clustering is proposed for feature selection. Effectiveness of the proposed method is compared with two existing methods of feature-selection entropy based and angular distance based clustering methods for bus voltage magnitude estimation at different loading conditions in the IEEE 30-bus system and a practical 75-bus Indian system. The PSHNN based on Euclidean distance based clustering method is found to be superior in terms of training time and error performance.