3D object classification with multi-view representation has become very popular, thanks to the progress on computer techniques and graphic hardware, and attracted much research attention in recent years. Regarding this task, there are mainly two challenging issues, i.e., the complex correlation among multiple views and the possible imbalance data issue. In this work, we propose to employ the hypergraph structure to formulate the relationship among 3D objects, taking the advantage of hypergraph on high-order correlation modelling. However, traditional hypergraph learning method may suffer from the imbalance data issue. To this end, we propose a vertex-weighted hypergraph learning algorithm for multi-view 3D object classification, introducing an updated hypergraph structure. In our method, the correlation among different objects is formulated in a hypergraph structure and each object (vertex) is associated with a corresponding weight, weighting the importance of each sample in the learning process. The learning process is conducted on the vertex-weighted hypergraph and the estimated object relevance is employed for object classification. The proposed method has been evaluated on two public benchmarks, i.e., the NTU and the PSB datasets. Experimental results and comparison with the state-of-the-art methods and recent deep learning method demonstrate the effectiveness of our proposed method.