Visible infrared person re-identification (VI-ReID) exposes considerable challenges because of the modality gaps between the person images captured by daytime visible cameras and nighttime infrared cameras. Several fully-supervised VI-ReID methods have improved the performance with extensive labeled heterogeneous images. However, the identity of the person is difficult to obtain in real-world situations, especially at night. Limited known identities and large modality discrepancies impede the effectiveness of the model to a great extent. In this paper, we propose a novel Semi-Supervised Learning framework with Heterogeneous Distribution Consistency (HDC-SSL) for VI-ReID. Specifically, through investigating the confidence distribution of heterogeneous images, we introduce a Gaussian Mixture Model-based Pseudo Labeling (GMM-PL) method, which adaptively adjusts different thresholds for each modality to label the identity. Moreover, to facilitate the representation learning of unutilized data whose prediction is lower than the threshold, Modality Consistency Regularization (MCR) is proposed to ensure the prediction consistency of the cross-modality pedestrian images and handle the modality variance. Extensive experiments with different label settings on two VI-ReID datasets demonstrate the effectiveness of our method. Particularly, HDC-SSL achieves competitive performance with state-of-the-art fully-supervised VI-ReID methods on RegDB dataset with only 1 visible label and 1 infrared label per class.