Merchants of e-commerce Websites expect recommender systems to entice more consumption which is highly correlated with the customers' purchasing propensity. However, most existing recommender systems focus on customers' general preference rather than purchasing propensity often governed by instant demands which we deem to be well conveyed by the questions asked by customers. A typical recommendation scenario is: Bob wants to buy a cell phone which can play the game PUBG. He is interested in HUAWEI P20 and asks “can PUBG run smoothly on this phone?” under it. Then our system will be triggered to recommend the most eligible cell phones to him. Intuitively, diverse user questions could probably be addressed in reviews written by other users who have similar concerns. To address this recommendation problem, we propose a novel Question-Driven Attentive Neural Network (QDANN) to assess the instant demands of questioners and the eligibility of products based on user generated reviews, and do recommendation accordingly. Without supervision, QDANN can well exploit reviews to achieve this goal. The attention mechanisms can be used to provide explanations for recommendations. We evaluate QDANN in three domains of Taobao. The results show the efficacy of our method and its superiority over baseline methods.