As a mathematical tool of representing the high-order relationship among multiple data objectives naturally, hypergraphs exhibit significant advantages compared to traditional graph-based machine learning methods. The premise of hypergraph-based learning paradigm lies in constructing hypergraph that can reflect the high-order relationships via hypergraph learning methods. However, the lack of robustness of the existing hypergraph learning methods in dealing with noise and data corruption limits their real application effects. To address this issue, a hypergraph learning method via block diagonal representation was proposed. In the method, an objective function of data reconstruction introducing the block diagonal constraint was optimized, and hyperedges were generated and the hyperedge weights were set using the obtained reconstruction coefficients. Experimental results on two image datasets adding noise demonstrate that compared with CR-HG (CorrentRopy-induced low-rank HyperGraph) method, the proposed method achieves improvements of 2.6 and 1.0 percentage points in Normalized Mutual Information (NMI) on the Coil20 image set with 40% Gaussian noise ratio and 30% salt-and-pepper noise density, respectively. Additionally, on the USPS image set with 40% Gaussian noise ratio and 30% salt-and-pepper noise density, the proposed method increases the Classification Accuracy for Classification（ACC） by 2.1 and 1.1 percentage points, respectively. It can be seen that the learning performance of the proposed method is superior to that of the existing mainstream hypergraph learning methods.