Next (or successive) point-of-interest (POI) recommendation has attracted increasing attention in recent years. Most of the previous studies attempted to incorporate the spatiotemporal information and sequential patterns of user check-ins into recommendation models to predict the target user's next move. However, none of these approaches utilized the social influence of each user's friends. In this study, we discuss a new topic of next POI recommendation and present a deep attentive network for social-aware next POI recommendation called DAN-SNR. In particular, the DAN-SNR makes use of the self-attention mechanism instead of the architecture of recurrent neural networks to model sequential influence and social influence in a unified manner. Moreover, we design and implement two parallel channels to capture short-term user preference and long-term user preference as well as social influence, respectively. By leveraging multi-head self-attention, the DAN-SNR can model long-range dependencies between any two historical check-ins efficiently and weigh their contributions to the next destination adaptively. Also, we carried out a comprehensive evaluation using large-scale real-world datasets collected from two popular location-based social networks, namely Gowalla and Brightkite. Experimental results indicate that the DAN-SNR outperforms seven competitive baseline approaches regarding recommendation performance and is of high efficiency among six neural-network- and attention-based methods.