In recent years recurrent neural network language models (RNNLMs) have been successfully applied to a range of tasks including speech recognition. However, an important issue that limits the quantity of data used, and their possible application areas, is the computational cost in training. A significant part of this cost is associated with the softmax function at the output layer, as this requires a normalization term to be explicitly calculated. This impacts both the training and testing speed, especially when a large output vocabulary is used. To address this problem, noise contrastive estimation (NCE), is used in RNNLM training in this paper. It does not require the above normalization during both training and testing and is insensitive to the output layer size. On a large vocabulary conversational telephone speech recognition task, a doubling in training speed and 56 time speed up in test time evaluation were obtained.