Coupled training of dimensionality reduction and classifica- Tion is proposed previously to improve the prediction per- formance for single-label problems. Following this line of research, in this paper, we introduce a novel Bayesian su- pervised multilabel learning method that combines linear di- mensionality reduction with linear binary classification. We present a deterministic variational approximation approach to learn the proposed probabilistic model for multilabel clas- sification. We perform experiments on four benchmark mul- Tilabel learning data sets by comparing our method with four baseline linear dimensionality reduction algorithms. Exper- iments show that the proposed approach achieves good per- formance values in terms of hamming loss, macro F1, and micro F1 on held-out test data. The low-dimensional em- beddings obtained by our method are also very useful for exploratory data analysis.