Recently, owing to the great advances in Web 2.0 and mobile devices, various online commercial services have emerged. Recommendation systems play an important role in dealing with abundant product information from massive numbers of online e-commerce transactions. Providing an accurate recommendation at the correct time to customers can contribute to a surge in business success. In this paper, an adaptive temporal-concept drift learning-based recommendation system, ATCRec, is developed for precisely tackling the sequential recommendation problem. We embed sequences of items into the latent spaces and learn both general preferences and sequential patterns concurrently via a recurrent neural network. Specifically, ATCRec captures dynamic changes in the temporal and concept drift contexts by modifying the gate units in a traditional recurrent neural network. The proposed model provides a unified and flexible network structure to learn and reveal the opaque variation of user preferences over time. We evaluate the robustness and performance of ATCRec on two real-world datasets, and the experimental results demonstrate that ATCRec consistently outperforms existing sequential recommendation approaches on various metrics. This indicates that integrating users"e temporal information and concept drift variation through time are indispensable in improving the performance of recommendation systems.