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 \emph{complete} supervised information, while in reality, annotation information may be \emph{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 \emph{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.