Abstract Label distribution learning (LDL) assumes labels can be associated to an instance to some degree, thus it can learn the relevance of a label to a particular instance. Although LDL has got successful practical applications, one problem with existing LDL methods is that they are designed for data with complete supervised information, while in reality, annotation information may be incomplete, because assigning each label a real value to indicate its association with a particular instance will result in large cost in labor and time. In this paper, we will solve LDL problem when given incomplete supervised information. We propose an objective based on trace norm minimization to exploit the correlation between labels. We develop a proximal gradient descend algorithm and an algorithm based on alternating direction method of multipliers. Experiments validate the effectiveness of our proposal