Summary: In this paper, we consider a class of semi-supervised metric learning problems. Due to the explosion in size and complexity of datasets, it is increasingly important to consider the sparse of metric learning. We add the constraint of sparse for the model of semi-supervised metric learning. To be easy to deal with the sparse constraint, we apply the Frobenius norm to define the sparse and transform it into the objective function of model by using the penalty parameter. Next we present an accelerated projection gradient algorithm, which is originally designed for convex smooth optimization in Euclidean space, over a positive definite matrix group. We analyze the convergence of our algorithm. Finally, we show the numerical test to demonstrate the effectiveness of the proposed algorithm.