With the advancement of mobile technology, Point of Interest (POI) recommendation systems in Location-based Social Networks (LBSN) have brought numerous benefits to both users and companies. Many existing works employ Knowledge Graph (KG) to alleviate the data sparsity issue in LBSN. These approaches primarily focus on modeling the pair-wise relations in LBSN to enrich the semantics and thereby relieve the data sparsity issue. However, existing approaches seldom consider the hyper-relations in LBSN, such as the mobility relation (a 3-ary relation: user-POI-time). This makes the model hard to exploit the semantics accurately. In addition, prior works overlook the rich structural information inherent in KG, which consists of higher-order relations and can further alleviate the impact of data sparsity.To this end, we propose a Hyper-Relational Knowledge Graph Neural Network (HKGNN) model. In HKGNN, a Hyper-Relational Knowledge Graph (HKG) that models the LBSN data is constructed to maintain and exploit the rich semantics of hyper-relations. Then we proposed a Hypergraph Neural Network to utilize the structural information of HKG in a cohesive way. In addition, a self-attention network is used to leverage sequential information and make personalized recommendations. Furthermore, side information, essential in reducing data sparsity by providing background knowledge of POIs, is not fully utilized in current methods. In light of this, we extended the current dataset with available side information to further lessen the impact of data sparsity. Results of experiments on four real-world LBSN datasets demonstrate the effectiveness of our approach compared to existing state-of-the-art methods.