With the prevalence of location based services, activity trajectories are being generated at a rapid pace. The activity trajectory data enriches traditional trajectory data with semantic activities of users, which not only shows where the users have been, but also the preference of users. However, the large volume of data is expensive for people to explore. To address this issue, we study the problem of Diversity-aware Activity Trajectory Selection (DaATS). Given a region of interest for a user, it finds a small number of representative activity trajectories that can provide the user with a broad coverage of different aspects of the region. The problem is challenging in both the efficiency of trajectory similarity computation and subset selection. To tackle the two challenges, we propose a novel solution by: (1) exploiting a deep metric learning method to speedup the similarity computation; and (2) proving that DaATS is an NP-hard problem, and developing an efficient approximation algorithm with performance guarantees. Experiments on two real-world datasets show that our proposal significantly outperforms state-of-the-art baselines.