Unsupervised person re-identification (Re-ID) has made significant progress by leveraging valuable pseudo labels from completely unlabeled data. However, the predominant use of pseudo labels heavily relies on clustering results, which may lead to the accumulation of supervision deviation due to inevitable noise. In this paper, we propose a novel framework, namely Dual Knowledge Distillation on Multiview Pseudo Labels (DKD-MPL), to address this challenge. Specifically, the proposed DKD-MPL framework consists of two modules: Global Knowledge Distillation (GKD) and Self-Knowledge Distillation (SKD). In the GKD module, the pseudo labels obtained from the epoch-wise clustering procedure serve as the logits for the teacher model, while the mini-batch query images' pseudo labels act as the logits for the student model. Within the SKD module, we facilitate self-knowledge distillation by considering the pseudo labels generated by positive anchors and query images as two augmentations of the mini-batch data. As a result, DKD-MPL facilitates the exploitation of both global and local complementary knowledge across different views of pseudo labels, thereby mitigating supervision deviation. To demonstrate the effectiveness of DKD-MPL, we provide a theoretical analysis of the proposed loss and conduct extensive experiments on four popular datasets, e.g., Market-1501, DukeMTMC-reID, MSMT17, and VeRi-776. The results indicate that our method surpasses unsupervised approaches and achieves comparable performance to supervised person Re-ID methods.