Visible-Infrared Person Re-identification (VI-ReID) is a challenging cross-modal pedestrian retrieval task, due to significant intra-class variations and cross-modal discrepancies among different cameras. Existing works mainly focus on embedding images of different modalities into a unified space to mine modality-shared features. They only seek distinctive information within these shared features, while ignoring the identity-aware useful information that is implicit in the modality-specific features. To address this issue, we propose a novel Implicit Discriminative Knowledge Learning (IDKL) network to uncover and leverage the implicit discriminative information contained within the modality-specific. First, we extract modality-specific and modality-shared features using a novel dual-stream network. Then, the modality-specific features undergo purification to reduce their modality style discrepancies while preserving identity-aware discriminative knowledge. Subsequently, this kind of implicit knowledge is distilled into the modality-shared feature to enhance its distinctiveness. Finally, an alignment loss is proposed to minimize modality discrepancy on modality-shared features. Extensive experiments on multiple public datasets demonstrate the superiority of IDKL network over the state-of-the-art methods.