Augmented Reality (AR) offers new capabilities for blurring the boundaries between physical reality and digital media. However, the capabilities of integrating web contents and AR remain underexplored. This paper presents an AR web browser with an integrated context-aware AR-to-Web content recommendation service named as A2W browser, to provide continuously user-centric web browsing experiences driven by AR headsets. We implement the A2W browser on an AR headset as our demonstration application, demonstrating the features and performance of A2W framework. The A2W browser visualizes the AR-driven web contents to the user, which is suggested by the content-based filtering model in our recommendation system. In our experiments, 20 participants with the adaptive UIs and recommendation system in A2W browser achieve up to 30.69% time saving compared to smartphone conditions. Accordingly, A2W-supported web browsing on workstations facilitates the recommended information leading to 41.67% faster reaches to the target information than typical web browsing.