Multi-label classification is a special learning task where each instance may be associated with multiple labels simultaneously. There are two main challenges: (a) discovering and exploiting the label correlations automatically, and (b) separating the relevant labels from the irrelevant labels of each instance effectively. Nevertheless, many existing multi-label classification algorithms fail to deal with both challenges at the same time. In this paper, we integrate multi-label classification, label correlations and threshold calibration into a unified learning framework, and propose calibrated multi-label classification with label correlations, named CMLLC. Specifically, we firstly introduce a label covariance matrix to characterize the label correlations and a virtual label to calibrate label decision threshold of each instance. Secondly, the framework of our CMLLC model is constructed for joint learning of the label correlations and model parameters corresponding to each label and the virtual label. Lastly, the optimization problem is jointly convex and solved by an alternating iterative method. Experimental results on sixteen multi-label benchmark datasets in terms of five evaluation criteria demonstrate that CMLLC outperforms the state-of-the-art multi-label classification algorithms.