A recurrent neural network language model (RNN-LM) can use a long word context more than can an n-gram language model, and its effective has recently been shown in its accomplishment of automatic speech recognition (ASR) tasks. However, the training criteria of RNN-LM are based on cross entropy (CE) between predicted and reference words. In addition, unlike the discriminative training of acoustic models and discriminative language models (DLM), these criteria do not explicitly consider discriminative criteria calculated from ASR hypotheses and references. This paper proposes a discriminative training method for RNN-LM by additionally considering a discriminative criterion to CE. We use the log-likelihood ratio of the ASR hypotheses and references as an discriminative criterion. The proposed training criterion emphasizes the effect of improperly recognized words relatively compared to the effect of correct words, which are discounted in training. Experiments on a large vocabulary continuous speech recognition task show that our proposed method improves the RNN-LM baseline. In addition, combining the proposed discriminative RNN-LM and DLM further shows its effectiveness.