360-degree video streaming, which is becoming more and more popular as the fast development of VR/AR applications nowadays due to the immersive viewing experience it can offer, poses enormous challenges to the current network infrastructure in terms of high bandwidth and low latency requirements. To address this problem and to ensure the QoE (quality of experience) of end-users, this paper presents CUBIST, a method and system for high-quality 360-degree video streaming in networks with cache nodes at the edge. To the best of our knowledge, it is the first tile-based edge caching solution that incorporates proactive tile prefetching and hierarchical cache organization into reactive caching to maximize the caching benefit while reducing the cost of 360-degree video streaming. Experimental results show that CUBIST can achieve a cache hit ratio of 87 % and improve the effective video bitrate by 12.9 % with most rate transitions being small when compared with the latest FoV-aware edge caching scheme.