Adaptive bitrate (ABR) streaming is the de facto solution for achieving smooth viewing experiences under unstable network conditions. However, most of the existing rate adaptation approaches for ABR are content-agnostic, without considering the semantic information of the video content. Nevertheless, semantic information largely determines the informativeness and interestingness of the video content, and consequently affects the QoE for video streaming. One common case is that the user may expect higher quality for the parts of video content that are more interesting or informative so as to reduce video distortion and information loss, given that the overall bitrate budgets are limited. This creates two main challenges for such a problem: First, how to determine which parts of the video content are more interesting? Second, how to allocate bitrate budgets for different parts of the video content with different significances? To address these challenges, we propose a Content-of-Interest (CoI) based rate adaptation scheme for ABR. We first design a deep learning approach for recognizing the interestingness of the video content, and then design a Deep Q-Network (DQN) approach for rate adaptation by incorporating video interestingness information. The experimental results show that our method can recognize video interestingness precisely, and the bitrate allocation for ABR can be aligned with the interestingness of video content while not compromising the performances on objective QoE metrics.