Motivated by the remarkable successes of graph-based transduction (GT) and sparse representation (SR), we present a classifier named sparse graph-based classifier (SGC) for image classification. In SGC, SR is leveraged to measure the correlation (similarity) of every two samples and a graph is constructed for encoding these correlations. Then the Laplacian eigenmapping is adopted for deriving the graph Laplacian of the graph. Finally, SGC can be obtained by plugging the graph Laplacian into the conventional GT framework. In the image classification procedure, SGC utilizes the correlations which are encoded in the learned graph Laplacian, to infer the labels of unlabeled images. SGC inherits the merits of both GT and SR. Compared to SR, SGC improves the robustness and the discriminating power of GT. Compared to GT, SGC sufficiently exploits the whole data. Therefore, it alleviates the undercomplete dictionary issue suffered by SR. Four popular image databases are employed for evaluation. The results demonstrate that SGC can achieve a promising performance in comparison with the state-of-the-art classifiers, particularly in the small training sample size case and the noisy sample case.