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Conventional nonnegative matrix factorization and its variants cannot separate the noise data space into a clean space and learn an effective low-dimensional subspace from Salt and Pepper noise or Contiguous Occlusion. This paper proposes a weighted nonnegative matrix factorization (WNMF) to improve the robustness of existing nonnegative matrix factorization. In WNMF, a weighted graph is constructed to label the uncorrupted data as 1 and the corrupted data as 0, and an effective matrix factorization model is proposed to recover the noise data and achieve clustering from the recovered data. Extensive experiments on the image datasets corrupted by Salt and Pepper noise or Contiguous Occlusion are presented to demonstrate the effectiveness and robustness of the proposed method in image inpainting and clustering.