Convolutional neural networks with multiple branches have recently been proved highly effective in person re-identification (re-ID). Researchers design multi-branch networks using part models, yet they always attribute the effectiveness to multiple parts. In addition, existing multi-branch networks always have isomorphic branches, which lack structural diversity. In order to improve this problem, we propose a novel Heterogeneous Branch and Multi-level Classification Network (HBMCN), which is designed based on the pre-trained ResNet-50 model. A new heterogeneous branch, SE-Res-Branch, is proposed based on the SE-Res module, which consists of the Squeeze-and-Excitation block and the residual block. Furthermore, a new multi-level classification joint objective function is proposed for the supervised learning of HBMCN, whereby multi-level features are extracted from multiple high-level layers and concatenated to represent a person. Based on three public person re-ID benchmarks (Market1501, DukeMTMC-reID and CUHK03), experimental results show that the proposed HBMCN reaches 94.4%, 85.7% and 73.8% in Rank-1, and 85.7%, 74.6% and 69.0% in mAP, achieving a state-of-the-art performance. Further analysis demonstrates that the specially designed heterogeneous branch performs better than an isomorphic branch, and multi-level classification provides more discriminative features compared to single-level classification. As a result, HBMCN provides substantial further improvements in person re-ID tasks.