A connectional brain template (CBT) is a fingerprint graph-based representation of a population of brain networks, serving as an ‘average’ connectome. CBTs are essential for creating representative maps of brain connectivity in both typical and atypical populations, facilitating the identification of deviations from healthy brain structures. However, traditional methods for generating CBTs often rely on linear averaging and pairwise relationships, which fail to capture the complex, high-order interactions within brain networks, particularly in multi-view brain networks where the brain is encoded in a set of connectivity matrices (i.e., tensor). To address these limitations, we propose a novel Generative Hypergraph Neural Network (Gen-HNN) for learning hyper connectional brain templates (HCBTs). Gen-HNN leverages hypergraphs to capture higher-order relationships, utilizing hyperedge convolution operations based on the hypergraph Laplacian to process and integrate multi-view brain data into a cohesive HCBT. Our model overcomes the limitations of existing methods by effectively handling non-linear patterns and preserving the topological properties of brain networks. We conducted extensive experiments, demonstrating that Gen-HNN significantly outperforms state-of-the-art methods in terms of both representativeness and discriminative power. Our Gen-HNN code is available at https://github.com/basiralab/Gen-HNN .