Sequential recommendation (SR) learns from the temporal dynamics of user-item interactions to predict the next ones. Fairness-aware recommendation mitigates a variety of algorithmic biases in the learning of user preferences. This paper aims at bringing a marriage between SR and algorithmic fairness. We propose a novel fairness-aware sequential recommendation task, in which a new metric, interaction fairness, is defined to estimate how recommended items are fairly interacted by users with different protected attribute groups. We propose a multi-task learning based deep end-to-end model, FairSR, which consists of two parts. One is to learn and distill personalized sequential features from the given user and her item sequence for SR. The other is fairness-aware preference graph embedding (FPGE). The aim of FPGE is two-fold: incorporating the knowledge of users' and items' attributes and their correlation into entity representations, and alleviating the unfair distributions of user attributes on items. Extensive experiments conducted on three datasets show FairSR can outperform state-of-the-art SR models in recommendation performance. In addition, the recommended items by FairSR also exhibit promising interaction fairness.