POI (Point-of-interest) prediction is a significant issue in recent years. It can not only enhance user experience in location-based service and apps but also promote the perceived ability of business to potential consumers. However, the accuracy of POI prediction is seriously dragged down by data sparsity. To remedy the problem, recent researches studied various context factors. But their models only focus on part of context factors and are not well compatible for new factors. To address these challenges, in this paper, we first propose a unified flexible model ‘Dynamic Metric Embedding with temporal (T) and spatial (S) factors’ (DME-TS), since it is based on metric embedding (ME), which can map various factors into a unified Euclidean space and learn them collectively to resolve data sparsity. At the same time, temporal factors are studied systemically from three aspects: dynamic personal interest, temporal non-uniformness, temporal sequentiality. In order to represent each factor in Euclidean space, we propose several targeted methods. First, Long Short Term Memory is brought into metric embedding to depict user's dynamic interest. Then, to character temporal non-uniformness, we develop a self-attention method, which can estimate the temporal relationship between user's behaviors. Besides, to depict temporal sequentiality and spatial influence, Euclidean distance and spatial distance of successive check-ins are utilized. Next, these factors are combined into metric embedding, forming our model DME-TS. Finally, experiments are conducted on two publicly available datasets. The experimental results demonstrate the effectiveness of DME-TS, which improves the state-of-the-art method performance nearly 10%. © 2018 Elsevier B.V.