In this paper, we study the feasibility of using a neural network to learn a fitness function for a machine translation system based on a genetic algorithm termed GAMaT. The neural network is learned on features extracted from pairs of source sentences and their translations. The fitness function is trained in order to estimate the BLEU of a translation as precisely as possible. The estimator has been trained on a corpus of more than 1.3 million data. The performance is very promising: the difference between the real BLEU and the one given by the estimator is equal to 0.12 in terms of Mean Absolute Error.