Session-based Recommendation (SR) is the task of recommending the next item based on previously recorded user interactions. In this work, we study SR in a practical streaming scenario, namely Streaming Session-based Recommendation (SSR), which is a more challenging task due to (1) the uncertainty of user behaviors, and (2) the continuous, large-volume, high-velocity nature of the session data. Recent studies address (1) by exploiting the attention mechanism in Recurrent Neural Network (RNN) to better model the user's current intent, which leads to promising improvements. However, the proposed attention models are based solely on the current session. Moreover, existing studies only perform SR under static offline settings and none of them explore (2). In this work, we target SSR and propose a Streaming Sessionbased Recommendation Machine (SSRM) to tackle these two challenges. Specifically, to better understand the uncertainty of user behaviors, we propose a Matrix Factorization (MF) based attention model, which improves the commonly used attention mechanism by leveraging the user's historical interactions. To deal with the largevolume and high-velocity challenge, we introduce a reservoir-based streaming model where an active sampling strategy is proposed to improve the efficiency of model updating. We conduct extensive experiments on two real-world datasets. The experimental results demonstrate the superiority of the SSRM method compared to several state-of-the-art methods in terms of MRR and Recall.