Abstract: With the widespread use of smart phones and mobile Internet, social network users have generated massive geo-tagged tweets, photos and videos to form lots of informative trajectories which reveal not only their spatio-temporal dynamics, but also their activities in the physical world. Existing spatial trajectory query studies mainly focus on analyzing the spatio-temporal properties of the users' trajectories, while leaving the understanding of their activities largely untouched. In this paper, we incorporate the semantics of the activity information embedded in trajectories into query modelling and processing, with the aim of providing end users more informative and meaningful results. To this end, we propose a novel trajectory query that not only considers the spatio-temporal closeness but also, more importantly, leverages a proven technique in text mining field, probabilistic topic modelling, to capture the semantic relatedness of the activities between the data and query. To support efficient query processing, we design a hierarchical grid-based index by integrating the probabilistic topic distribution on the substructures of trajectories and their spatio-temporal extent at the corresponding level of the index hierarchy. This specialized structure enables a top-down search algorithm to traverse the index while pruning unqualified trajectories in spatial and topical dimensions simultaneously. The experimental results on real-world datasets demonstrate the good efficiency and scalability performance of the proposed indices and trajectory search methods.