Friend recommendation from human mobility is a vital real-world application of location-based social networks (LBSN). It is necessary to recognize patterns from human mobility to assist friend recommendation because previous works have shown complex relations between them. However, most of previous works either modelled social networks and user trajectories separately, or only used classical simple graph-based methods with an edge linking two nodes that cannot fully model the complex data structure of LBSN. Inspired by the fact that hyperedges can connect multiple nodes of different types, we model user trajectories and check-in records as hyperedges in a novel heterogeneous LBSN hypergraph to represent complex spatio-temporal information. And then, we design a type-specific attention mechanism for an end-to-end trainable heterogeneous hypergraph neural network (HHGNN) with supervised contrastive learning, which can learn hypergraph node embedding for the next friend recommendation task. At last, our model HHGNN outperforms the state-of-the-art methods on four real-world city datasets, while ablation studies also confirm the effectiveness of each model part.