Many batch learning algorithms have been introduced for offline multi-label classification (MLC) over the years. However, the increasing data volume in many applications such as social networks, sensor networks, and traffic monitoring has posed many challenges to batch MLC learning. For example, it is often expensive to re-train the model with the newly arrived samples, or it is impractical to learn on the large volume of data at once. The research on incremental learning is therefore applicable to a large volume of data and especially for data stream. In this study, we develop a Bayesian-based method for learning from multi-label data streams by taking into consideration the correlation between pairs of labels and the relationship between label and feature. In our model, not only the label correlation is learned with each arrived sample with ground truth labels but also the number of predicted labels are adjusted based on Hoeffding inequality and the label cardinality. We also extend the model to handle missing values, a problem common in many real-world data. To handle concept drift, we propose a decay mechanism focusing on the age of the arrived samples to incrementally adapt to the change of data. The experimental results show that our method is highly competitive compared to several well-known benchmark algorithms under both the stationary and concept drift settings.