Hypergraph learning has been widely exploited in various image processing applications, due to its advantages in modeling the high-order information. Its efficacy highly depends on building an informative hypergraph structure to accurately and robustly formulate the underlying data correlation. However, the existing hypergraph learning methods are sensitive to non- Gaussian noise, which hurts the corresponding performance. In this paper, we present a noise-resistant hypergraph learning model, which provides superior robustness against various non- Gaussian noises. In particular, our model adopts low-rank representation to construct a hypergraph, which captures the globally linear data structure as well as preserving the grouping effect of highly-correlated data. We further introduce a correntropyinduced local metric to measure the reconstruction errors, which is particularly robust to non-Gaussian noises. Finally, the Frobenious-norm based regularization is proposed to combine with the low-rank regularizer, which enables our model to regularize the singular values of the coefficient matrix. By such, the non-zero coefficients are selected to generate a hyperedge set as well as the hyperedge weights. We have evaluated the proposed hypergraph model in the tasks of image clustering and semi-supervised image classification. Quantitatively, our scheme significantly enhances the performance of the state-of-the-art hypergraph models on several benchmark datasets.