With the recent surge of location based social networks (LBSNs), activity data of millions of users has become attainable. This data contains not only spatial and temporal stamps of user activity, but also its semantic information. LBSNs can help to understand mobile users' spatial temporal activity preference (STAP), which can enable a wide range of ubiquitous applications, such as personalized context-aware location recommendation and group-oriented advertisement. However, modeling such user-specific STAP needs to tackle high-dimensional data, i.e., user-location-time-activity quadruples, which is complicated and usually suffers from a data sparsity problem. In order to address this problem, we propose a STAP model. It first models the spatial and temporal activity preference separately, and then uses a principle way to combine them for preference inference. In order to characterize the impact of spatial features on user activity preference, we propose the notion of personal functional region and related parameters to model and infer user spatial activity preference. In order to model the user temporal activity preference with sparse user activity data in LBSNs, we propose to exploit the temporal activity similarity among different users and apply nonnegative tensor factorization to collaboratively infer temporal activity preference. Finally, we put forward a context-aware fusion framework to combine the spatial and temporal activity preference models for preference inference. We evaluate our proposed approach on three real-world datasets collected from New York and Tokyo, and show that our STAP model consistently outperforms the baseline approaches in various settings