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When a group of lifts serve together it is important coordinate the movements of the individual lifts in such a way that the lift group should operate efficiently. This is dealt with elevator control systems, which have become more and more complicated due to their nature of intelligence. Neural networks, which have been proved to be successful in many fields, can also be applied to the next stopping floor problem in elevator traffic control algorithms. In particular, neural networks can offer better solutions to the next stopping floor problem when compared to the classical traffic control methods. Elevator control algorithms based on neural networks can dynamically learn the behavior of an elevator system and predict the next floors to stop by considering what has been learnt by processing the changes in passenger service demand pattern. Neural networks have been used to build a one step ahead predictor for elevator traffic pattern. In this paper a neural network algorithm is apllied to obtain a better solution to the next stopping floor problem in elevator group control and its learning capability is assessed by means of simulation software developed.