In this paper, joint learning of multi-label classification and label correlations (JMLLC) is proposed. In JMLLC, a directed conditional dependency network is constructed based on class label variables. This not only enables joint learning of independent label classifiers to enhance the performance of label classifiers, but also allows joint learning of label classifiers and label correlations, thereby making the learned label correlations more accurate. JMLLC-LR (JMLLC with logistic regression) and JMLLC-LS (JMLLC with least squares), are proposed respectively by adopting two different loss functions: logistic regression and least squares, and are both extended to the reproducing kernel Hilbert space (RKHS). Finally, both JMLLC-LR and JMLLC-LS can be solved by alternating solution approaches. Experimental results on twenty benchmark data sets based on five different evaluation criteria demonstrate that JMLLC outperforms the state-of-the-art MLL algorithms.