In recent years, a variety of feature selection algorithms based on subspace learning have been proposed. However, such methods typically do not exploit information about the underlying geometry of the data. To overcome this shortcoming, we propose a novel algorithm called subspace learning-based graph regularized feature selection (SGFS). SGFS builds on the feature selection framework of subspace learning, but extends it by incorporating the idea of graph regularization, in which a feature map is constructed on the feature space in order to preserve geometric structure information on the feature manifold. Additionally, the L2,1-norm is used to constrain the feature selection matrix to ensure the sparsity of the feature array and avoid trivial solutions. The resulting method can provide more accurate discrimination information for feature selection. We evaluate SGFS by comparing it against five other state-of-the-art algorithms from the literature, on twelve publicly available benchmark data sets. Empirical results suggest that SGFS is more effective than the other five feature selection algorithms.