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Nonnegative matrix factorization-based image representation algorithms have been widely applied to deal with high-dimensional data in the past few years. In this paper, we propose a graph regularized constrained nonnegative matrix factorization with L_p Smoothing (GCNMFS) for image representation. Specifically, the main contributions of the proposed GCNMFS method include as follows: firstly, the geometric manifold structure hidden in data is effectively exploited by adopting a graph regularizer. Secondly, the label information of labeled samples is incorporated into the model of NMF without additional parameters. Finally, the L_p smoothness constraint is used to constrain the basis matrix, and thus a smooth and more accurate solution is produced. Moreover, an effective optimization scheme is presented to solve the proposed model. Extensive experiments on several image datasets show the proposed GCNMFS method can achieve better performance than other state-of-the-art methods in clustering.