Users prefer diverse recommendations over homogeneous ones. However, most previous work on Sequential Recommenders does not consider diversity, and strives for maximum accuracy, resulting in homogeneous recommendations. In this paper, we consider both accuracy and diversity by presenting an Attribute-aware Diversifying Sequential Recommender (ADSR). Specifically, ADSR utilizes available attribute information when modeling a user's sequential behavior to simultaneously learn the user's most likely item to interact with, and their preference of attributes. Then, ADSR diversifies the recommended items based on the predicted preference for certain attributes. Experiments on two benchmark datasets demonstrate that ADSR can effectively provide diverse recommendations while maintaining accuracy.