Multi-shot people re-identification in non overlapping camera networks is a major challenge. In this paper, we present a spatio-temporal covariance (STCovariance) descriptor which considers groups of pictures to implicitly encode the described human motion by the integration of time parameter. This parameter provides modeling capabilities of people motion added to appearance features. To deal with the changes of illumination, we integrate Local binary pattern (LBP) operator into the ST-Covariance descriptor. The new LBP based ST-covariance descriptor improves the people recognition performances in the case of multi-shot re-identification. The experiments conducted on "CAVIAR4REID" dataset showed these improvements. The people recognition rate in the first rank outperforms the other descriptors by more than 15%.