The existing nonnegative matrix factorization methods mainly focus on learning global structure of the data， while ignoring the learning of local information. Meanwhile， for those methods that attempt to exploit local similarity， the manifold learning is often adopted， which suffers some issues. To solve this problem， a new method named the robust nonnegative matrix factorization with local similarity learning （RLS-NMF） is proposed. In this paper， a new local similarity learning method is adopted， which is starkly different from the widely used manifold learning. Moreover， the new method can simultaneously learn the global structural information of the data， and thus exploit the intra-class similarity and the inter-class separability of the data. To address the issues of outliers and noise effects in real word applications， the l2,1 norm is used to fit the residuals to filter the redundant noise information， ensuring the robustness of the algorithm. Extensive experimental results show the superior performance of the proposed method on several benchmark datasets， further demonstrating its effectiveness.