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To tackle the challenge of vehicle re-identification (Re-ID) in complex lighting environments and diverse scenes, multi-spectral sources like visible and infrared information are taken into consideration due to their excellent complementary advantages. However, multi-spectral vehicle Re-ID suffers cross-modality discrepancy caused by heterogeneous properties of different modalities as well as a big challenge of the diverse appearance with different views in each identity. Meanwhile, diverse environmental interference leads to heavy sample distributional discrepancy in each modality. In this work, we propose a novel cross-directional consistency network to simultaneously overcome the discrepancies from both modality and sample aspects. In particular, we design a new cross-directional center loss to pull the modality centers of each identity close to mitigate cross-modality discrepancy, while the sample centers of each identity close to alleviate the sample discrepancy. Such strategy can generate discriminative multi-spectral feature representations for vehicle Re-ID. In addition, we design an adaptive layer normalization unit to dynamically adjust individual feature distribution to handle distributional discrepancy of intra-modality features for robust learning. To provide a comprehensive evaluation platform, we create a high-quality RGB-NIR-TIR multi-spectral vehicle Re-ID benchmark (MSVR310), including 310 different vehicles from a broad range of viewpoints, time spans and environmental complexities. Comprehensive experiments on both created and public datasets demonstrate the effectiveness of the proposed approach comparing to the state-of-the-art methods.