Hypergraph matching is a useful tool to find feature correspondence by considering higher-order structural information. Recently, the employment of deep learning has made great progress in the matching of graphs, suggesting its potential for hypergraphs. Hence, in this paper, we present the first, to our best knowledge, unified hypergraph neural network (HNN) solution for hypergraph matching. Specifically, given two hypergraphs to be matched, we first construct an association hypergraph over them and convert the hypergraph matching problem into a node classification problem on the association hypergraph. Then, we design a novel hypergraph neural network to effectively solve the node classification problem. Being end-to-end trainable, our proposed method, named HNN-HM, jointly learns all its components with improved optimization. For evaluation, HNN-HM is tested on various benchmarks and shows a clear advantage over state-of-the-arts.