As a popular dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in image classification. However, the NMF does not consider discriminant information from the data themselves. In addition, most NMF-based methods use the Euclidean distance as a metric, which is sensitive to noise or outliers in data. To solve these problems, in this paper, we introduce structural incoherence and low-rank to NMF and propose a novel nonnegative factorization method, called structurally incoherent low-rank NMF (SILR-NMF), in which we jointly consider structural incoherence and low-rank properties of data for image classification. For the corrupted data, we use the L-1 norm as a constraint to ensure the noise is sparse. SILR-NMF learns a clean data matrix from the noisy data by low-rank learning. As a result, the SILR-NMF can capture the global structure information of the data, which is more robust than local information to noise. By introducing the structural incoherence of the learned clean data, SILR-NMF ensures the clean data points from different classes are as independent as possible. To verify the performance of the proposed method, extensive experiments are conducted on six image databases. The experimental results demonstrate that our proposed method has substantial gain over existing NMF approaches.