The capability of extracting sequential patterns from the user-item interaction data is now becoming a key feature of recommender systems. Though it is important to capture the sequential effect, existing methods only focus on modelling the sparse item-wise sequential effect in user preference and only consider the homogeneous user interaction behaviors (i.e., a single type of user behavior). As a result, the data sparsity issue inevitably arises and makes the learned sequential patterns fragile and unreliable, impeding the sequential recommendation performance of existing methods. Hence, in this paper, we propose AIR, namely attentional intention-aware recommender systems to predict category-wise future user intention and collectively exploit the rich heterogeneous user interaction behaviors (i.e., multiple types of user behaviors). In AIR, we propose to represent user intention as an action-category tuple to discover category-wise sequential patterns and to capture varied effect of different types of actions for recommendation. A novel attentional recurrent neural network (ARNN) is proposed to model the intention migration effect and infer users' future intention. Besides, an intention-aware factorization machine (ITFM) is developed to perform intention-aware sequential recommendation. Experiments on two real-life datasets demonstrate the superiority and practicality of AIR in sequential top-k recommendation tasks.