We investigate sequence-discriminative training of long short-term memory recurrent neural networks using the maximum mutual information criterion. We show that although recurrent neural networks already make use of the whole observation sequence and are able to incorporate more contextual information than feed forward networks, their performance can be improved with sequence-discriminative training. Experiments are performed on two publicly available handwriting recognition tasks containing English and French handwriting. On the English corpus, we obtain a relative improvement in WER of over 11% with maximum mutual information (MMI) training compared to cross-entropy training. On the French corpus, we observed that it is necessary to interpolate the MMI objective function with cross-entropy.