Person re-identification is an important task in video surveillance systems. It consists in matching an image of a probe person among a gallery image set of people detected from a network of surveillance cameras with non-overlapping fields of view. The main challenge of person re-identification is to find image representations that are discriminating the per-sons' identities and that are robust to the viewpoint, body pose, illumination changes and partial occlusions. In this paper , we proposed a metric learning approach based on a deep neural network using a novel loss function which we call the Rank-Triplet loss. This proposed loss function is based on the predicted and ground truth ranking of a list of instances instead of pairs or triplets and takes into account the improvement of evaluation measures during training. Through our experiments on two person re-identification datasets, we show that the new loss outperforms other common loss functions and that our approach achieves state-of-the-art results on these two datasets.