Person re-identification (ReID) is a desirable yet challenging issue in computer vision, which has numerous potential applications in the public security area. In this paper, the information bottleneck (IB) theory is introduced to filter out the undiscriminating information and noise, and keep the distinctive information for persons, to identify the assigned person from the candidates. To meet the requirement of the IB theory, a dual-stream IB-enhanced (DSIB) ReID framework is proposed to make unentangled estimations of the expectation and variance of the feature map. Moreover, the unconditional feature distribution is relaxed from standard normal distribution to Gaussian distribution, to enrich the information contained in each feature channel. Comprehensive experiments are conducted with several baseline models on datasets MARS, LS-VID, iLiDS-VID, and PRID-2011. The results reveal that our proposed DSIB framework has improved the performance of all baseline models, and it outperforms most state-of-the-art methods in terms of mean average precision (mAP) and Rank-1 precision.