The recommender system (RS) is a well-known practical application of the state-of-the-art information filtering and machine learning technologies. Traditional recommendation approaches, including collaborative and content-based filtering techniques, have been widely employed to provide suggestions in RSs, where the user-item interaction matrix is the primary data source. In many application domains, interactions between users and items are more likely to be dynamic rather than static, and thus dynamic user behaviors should be taken into account when solving recommendation tasks in order to provide more accurate suggestions. In this work, we consider the sequentially ordered information from user-item interactions in the RSs where a sequence-based recommendation model is put forward with applications to the food recommendation scenario. Furthermore, the long short-term memory (LSTM) network is employed as the building block to establish such a recommendation model, and a collaborative filtering unit is adopted to make personalized food recommendation. The proposed LSTM-based RS is successfully applied to a real-world food recommendation data set. Experimental results demonstrate that the developed method outperforms some currently popular RSs in terms of precision, recall, mean average precision and mean reciprocal rank in food recommendation.