Point-of-Interest (POI) recommendation has been a trending research topic as it generates personalized suggestions on facilities for users from a large number of candidate venues. Since users' check-in records can be viewed as a long sequence, methods based on recurrent neural networks (RNNs) have recently shown promising applicability for this task. However, existing RNN-based methods either neglect users' long-term preferences or overlook the geographical relations among recently visited POIs when modeling users' short-term preferences, thus making the recommendation results unreliable. To address the above limitations, we propose a novel method named Long- and Short-Term Preference Modeling (LSTPM) for next-POI recommendation. In particular, the proposed model consists of a nonlocal network for long-term preference modeling and a geo-dilated RNN for short-term preference learning. Extensive experiments on two real-world datasets demonstrate that our model yields significant improvements over the state-of-the-art methods.