Most graph-based semi-supervised learning methods do not use the known label information and the label information obtained from the label propagation process when measuring the similarity between samples. At the same time, these methods have the measurement methods relatively fixed, which cannot effectively measure the similarity between data samples with complex and varied distribution structures. In order to solve the problems, a semi-supervised learning algorithm of graph based on label metric learning was proposed. Firstly, the similarity measurement method of samples was given, and then the similarity matrix was constructed. Secondly, labels were propagated based on the similarity matrix and k samples with low entropy were selected as the new obtained label information. Finally, the similarity measure method was updated by fully using all label information, and this process was repeated until all label information was learned. The proposed algorithm not only uses label information to improve the measurement method of similarity between samples, but also makes full use of intermediate results to reduce the demand for labeled data in the semi-supervised learning. Experimental results on six real datasets show that, compared with three traditional graph-based semi-supervised learning algorithms, the proposed algorithm achieves higher classification accuracy in more than 95% of the cases.