Cross-modal person re-identification (Re-ID) compensates for the supervision of suspicious persons under dark conditions and has important significance in real life. Existing related studies based on triplet loss adopt either too strong or too weak constraints to aggregate features, so in order to further improve accurate person Re-ID, this paper proposes a weighted regular heterogeneous-center loss, which adopts a weighted approach to adaptively keep the centers of person features of different identities away from each other while pulling the centers of same identities of different modalities closer. Besides, this paper also proposes a network for adaptive extraction of local features, which adaptively extracts local features through an attention mechanism, and then employs a combination of global features and local features to effectively enhance the robustness of person features and improve the detection accuracy of person Re-ID. Experiments on two publicly available cross-modal person re-identification datasets SYSU-MM01 and RegDB in this paper demonstrate the effectiveness of the proposed method, which achieves comparable or leading detection results compared with current mainstream algorithms.