The present work demonstrates the use of computationally inexpensive neural network (NN) potential for studying global optimizations and phase transitions in small to medium sized sodium clusters with DFT accuracy. Accuracy of NN potential has been tested by performing global optimizations in the size range of 16-40 atoms. We performed Monte Carlo (MC) simulations using NN potential to study the melting behaviour. Melting study in the size range of 20-40 atoms shows a characteristic premelting peak and a main melting peak. Our results using NN potentials support the idea of stepwise melting in small Na clusters (Aguado, 2011). (C) 2016 Elsevier B.V. All rights reserved.