Attributes are human-annotated semantic descriptions of label classes. In zero-shot learning (ZSL), they are often used to construct a semantic embedding for knowledge transfer from known classes to new classes. While collecting all attributes for the new classes is criticized as expensive, a subset of these attributes are often easy to acquire. In this paper, we extend ZSL methods to handle this partial set of observed attributes. We first recover the missing attributes through structured matrix completion. We use the low-rank assumption, and leverage properties of the attributes by extracting their rich semantic information from external sources. The resultant optimization problem can be efficiently solved with alternating minimization, in which each of its subproblems has a simple closed-form solution. The predicted attributes can then be used as semantic embeddings in ZSL. Experimental results show that the proposed method outperform existing methods in recovering the structured missing matrix. Moreover, methods using our predicted attributes in ZSL outperforms methods using either the partial set of observed attributes or other semantic embeddings.