Fine-grained website fingerprinting (WF) enables potential attackers to infer individual webpages on a monitored website that victims are visiting, by analyzing the resulting traffic protected by security protocols such as TLS. Most existing studies focus on WF at the granularity of website, which takes website homepages as their representatives for fingerprinting. Fine-grained WF can reveal more user privacy, such as online purchasing habits and video-viewing interests, and can also be employed for web censorship. Due to striking similarly of webpages on a same website, it is still an open problem to conduct fine-grained WF in an accurate and time-efficient way.In this paper, we propose BurNet, a fine-grained WF method using Convolutional Neural Networks (CNNs). To extract differences of similar webpages, we propose a new concept named unidirectional burst, which is a sequence of packets corresponding to a piece of HTTP message. BurNet takes as input unidirectional burst sequences, instead of bidirectional packet sequences, which makes it applicable to local and remote attack scenarios. BurNet employs CNNs to build a powerful classifier, where sophisticated architecture is designed to improve classification accuracy while reducing time complexity in training. We collect real-world datasets from two well-known websites and conduct extensive experiments to evaluate the performance of BurNet. The closed-world evaluation results show that BurNet outperforms the state-of-the-art methods in both attack scenarios. In the more realistic open-world setting, BurNet can achieve 0.99 precision and 0.99 recall. BurNet is also superior to its CNN-based counterparts in terms of training efficiency.