Classifier competence is critical important for dynamic classifier selection. This study proposes a semi-supervised learning algorithm to learn the competence of classifiers under the proposed optimization framework based on graph. First it constructs a graph based on the training data and some unlabeled data. Then it iteratively learns the competence of classifiers. The learned competence not just reflects the competitiveness of classifiers, but also varies smooth on the neighboring data. Experimental results on five different datasets show the dynamic classifier selection classification systems with the learned classifier competence perform better than the classification systems with local accuracy as the classifier competence.