Multi-label data stream usually contains noisy labels in the real-world applications, namely occuring in both relevant and irrelevant labels. However, existing online multi-label classification methods are mostly limited in terms of label quality and fail to deal with the case of noisy labels. On the other hand, the ground-truth label distribution may vary with the time changing, which is hidden in the observed noisy label distribution and difficult to track, posing a major challenge for concept drift adaptation. Motivated by this, we propose an online multi-label classification algorithm under Noisy and Changing Label Distribution (NCLD). The convex objective is designed to simultaneously model the label scoring and the label ranking for high accuracy, whose robustness to NCLD benefits from three novel works: 1) The local feature graph is used to reconstruct the label scores jointly with the observed labels, and an unbiased ranking loss is derived and applied to learn reliable ranking information. 2) By detecting the difference between two adjacent chunks with the unbiased label cardinality, we identify the change in the ground-truth label distribution and reset the ranking or all information learned from the past to match the new distribution. 3) Efficient and accurate updating is achieved based on the updating rule derived from the closed-form optimal model solution. Finally, empirical experimental results validate the effectiveness of our method in classifying instances under NCLD.