The exponential growth of Location-based Social Networks (LBSNs) has greatly stimulated the demand for precise location-based recommendation services. Next Point-of-Interest (POI) recommendation, which aims to provide personalised POI suggestions for users based on their visiting histories, has become a prominent component in location-based e-commerce. Recent POI recommenders mainly employ self-attention mechanism or graph neural networks to model complex high-order POI-wise interactions. However, most of them are merely trained on the historical check-in data in a standard supervised learning manner, which fail to fully explore each user's multi-faceted preferences, and suffer from data scarcity and long-tailed POI distribution, resulting in sub-optimal performance. To this end, we propose a Self-s}upervised Graph-enhanced POI Recommender (S2GRec) for next POI recommendation. In particular, we devise a novel Graph-enhanced Self-attentive layer to incorporate the collaborative signals from both global transition graph and local trajectory graphs to uncover the transitional dependencies among POIs and capture a user's temporal interests. In order to counteract the scarcity and incompleteness of POI check-ins, we propose a novel self-supervised learning paradigm in \ssgrec, where the trajectory representations are contrastively learned from two augmented views on geolocations and temporal transitions. Extensive experiments are conducted on three real-world LBSN datasets, demonstrating the effectiveness of our model against state-of-the-art methods.