This paper develops and presents a new neural network approach to model trip distribution, which is one of the important phases of conventional four-step travel demand modelling. The trip distribution problem has been investigated using back-propagation artificial neural networks in a number of studies and it was concluded that back-propagation artificial neural networks underperform when compared to traditional models. Such underperformance is due to the thresholding of the linearly combined inputs by utilising a non-linear function and carrying out this operation both in hidden and output layers. The proposed neural trip distribution model does not threshold the linearly combined outputs from the hidden layer. This makes it different from back-propagation artificial neural networks where combined inputs from the hidden layer are activated once more in the output layer. In addition, the neuron in the output layer is used as a summation unit in contrast to the methodologies cited in the neural network applications literature. At the same time, the bias neuron is not connected to the output neuron in the output layer. When this model is compared with various approaches such as the gravity model, modular neural networks and back-propagation neural networks, it was concluded that this new model provides better prediction of trip distribution and therefore, outperforms all the existing approaches.