Video surveillance has become more and more important in many domains for their security and safety. Person Re-Identification (Re-ID) is one of the most interesting subjects in this area. The Re-ID system is divided into two main stages: I) extracting feature representations to construct a person's appearance signature and ii) establishing the correspondence/matching by learning similarity metrics or ranking functions. However, appearance based person Re-Idis a challenging task due to similarity of human's appearance and visual ambiguities across different cameras. This paper provides a representation of the appearance descriptors, called signatures, for multi-shot Re-ID First, we will present the tracklets, i.e trajectories of persons. Then, we compute the signature and represent it based on the approach of Part Appearance Mixture (PAM). An evaluation of the quality of this signature representation is also described in order to essentially solve the problems of high variance in a person's appearance, occlusions, illumination changes and person's orientation/pose. To deal with variance in a person's appearance, we represent it as a set of multi-modal feature distributions modeled by Gaussian Mixture Model (GMM). Experiments and results on two public datasets and on our own dataset show good performance.