Currently, multi-label learning algorithms address classification more based on positive and negative logical labels with good results. However, logical labels inevitably lead to label misclassification. In addition, missing labels are widespread in the multi-label datasets. Recovering the missing labels and constructing soft labels that reflect the mapping relationship between instances and labels is an absolutely hard mission. Most of the existing algorithms can only solve one of these two problems. Unlike the existing algorithms, this paper proposes a soft-label recover based label-specific features learning (SLR-LSF) to solve above problems simultaneously. Firstly, the label correlation is calculated using the confidence matrix, which is combined with the label density information to obtain the membership degree of the soft label. Secondly, the membership degree and logical labels are combined to construct soft labels, which can help in recovering the missing labels. Finally, in the learning label-specific features process of soft labels, the local smoothness of the labels learned by manifold regularization is complemented by global label correlation. The classification performance and robustness of the algorithm are improved. To demonstrate the effectiveness of the proposed algorithm, comprehensive experiments are conducted on several data sets.