Multi-label learning is a very important machine learning paradigm. Traditional multi-label learning methods are designed in supervised or semi-supervised manner. Generally, they require accurate labeling of all or partial data into multiple categories. In many practical applications, it is difficult to obtain the label information with a large number of labels, which greatly restricts the promotion and application of multi-label learning. In contrast, label correlation, as a common weak supervision information, has lower requirements for labeling information. How to use label correlation for multi-label learning is an important but unstudied problem. This study proposes a method named weakly supervised multi-label learning using prior label correlation information (WSMLLC). This model restates the sample similarity by using label correlation, and can obtain label indicator matrix effectively, constrain the projection matrix of data by using prior information, and modify the indicator matrix by introducing regression terms. Compared with the existing methods, the outstanding advantage of WSMLLC model is that it can realize the label assignment of multi-label samples only by providing label correlation priors. Experimental results show that WSMLLC has obvious advantages over current advanced multi-label learning methods in the case of complete loss of label matrix.