The development of global positioning system stimulates the popularity of location-based social network (LBSN) services. With a large volume of data containing locations, texts, check-in information, and social relationships, spatial keyword queries in LBSNs have become increasingly complex. In this paper, we identify and solve the Social-based Time-aware Spatial Keyword Query (STSKQ) that returns the top-k objects by considering geo-spatial score, keywords similarity, visiting time score, and social relationship effect. To tackle STSKQ, we propose a two-layer hybrid index structure called Network Embedding Time-aware R-tree (NETR-Tree). In the user layer, we exploit the network embedding strategy to measure the relationship effect in users' relationship network. In the location layer, we build a Time-aware R-tree (TR-tree) considered spatial objects' spatiotemporal check-in information, and present a corresponding query processing algorithm. Finally, extensive experiments on two different real-life LBSNs demonstrate the effectiveness and efficiency of our methods, compared with existing state-of-the-art methods.