Unsupervised Visible-Infrared Person Re-identification (USVI-ReID) presents a formidable challenge, which aims to match pedestrian images across visible and infrared modalities without any annotations. Recently, clustered pseudo-label methods have become predominant in USVI-ReID, although the inherent noise in pseudo-labels presents a significant obstacle. Most existing works primarily focus on shielding the model from the harmful effects of noise, neglecting to calibrate noisy pseudo-labels usually associated with hard samples, which will compromise the robustness of the model. To address this issue, we design a Robust Pseudo-label Learning with Neighbor Relation (RPNR) framework for USVI-ReID. To be specific, we first introduce a straightforward yet potent Noisy Pseudo-label Calibration module to correct noisy pseudo-labels. Due to the high intra-class variations, noisy pseudo-labels are difficult to calibrate completely. Therefore, we introduce a Neighbor Relation Learning module to reduce high intra-class variations by modeling potential interactions between all samples. Subsequently, we devise an Optimal Transport Prototype Matching module to establish reliable cross-modality correspondences. On that basis, we design a Memory Hybrid Learning module to jointly learn modality-specific and modality-invariant information. Comprehensive experiments conducted on two widely recognized benchmarks, SYSU-MM01 and RegDB, demonstrate that RPNR outperforms the current state-of-the-art GUR with an average Rank-1 improvement of 10.3%. The source codes will be released soon.