Cross-modality person re-identification between the thermal and visible domains is extremely important for night-time surveillance applications. Existing works in this filed mainly focus on learning sharable feature representations to handle the cross-modality discrepancies. However, besides the cross-modality discrepancy caused by different camera spectrums, visible thermal person re-identification also suffers from large cross-modality and intra-modality variations caused by different camera views and human poses. In this paper, we propose a dual-path network with a novel bi-directional dual-constrained top-ranking loss to learn discriminative feature representations. It is advantageous in two aspects: 1) end-to-end feature learning directly from the data without extra metric learning steps, 2) it simultaneously handles the cross-modality and intra-modality variations to ensure the discriminability of the learnt representations. Meanwhile, identity loss is further incorporated to model the identity-specific information to handle large intra-class variations. Extensive experiments on two datasets demonstrate the superior performance compared to the state-of-the-arts.