Recently, sparse coding has achieved remarkable success in image representation tasks. In practice, the performance of clustering can be significantly improved if limited label information is incorporated into sparse coding. To this end, in this paper, a novel semi-supervised algorithm, called constrained sparse concept coding (CSCC), is proposed for image representation. CSCC considers limited label information into graph embedding as additional hard constraints, and hence obtains embedding results that are consistent with label information and manifold structure information of the original data. Therefore, CSCC can provide a sparse representation which explicitly utilizes the prior knowledge of the data to improve the discriminative power in clustering. Besides, a kernelized version of our proposed CSCC, namely kernel constrained sparse concept coding (KCSCC), is developed to deal with nonlinear data, which leads to more effective clustering performance. The experimental evaluations on the MNIST, PIE and Yale image sets show the effectiveness of our proposed algorithms.