With the improvement of network technology, it enables multimedia services to become more immersive and attractive. Multiview video streaming provides a scene captured by many cameras from different perspectives or viewpoints. This streaming application gives a freedom to the user to select any viewpoint freely, to be shown on the main video screen. In a bandwidth-limited environment, the video application may prioritize high-quality video for the main viewpoint. However, this can prevent a seamless transition between viewpoints during a viewpoint switch. In this work, we define viewpoint delay as transition delay and quality delay, which are related to switching response and quality smoothness during viewpoint switching, respectively. Then, we formulate multiview quality of experience (MV-QoE) as a metric to measure user engagement and satisfaction. To achieve high MV-QoE performance, we propose a quality-aware streaming adaptation to select the best quality combination between viewpoints. The algorithm is called multiview priority (MVP), which assigns different bandwidth priorities and quality targets between main viewpoint and sub-viewpoints. Specifically, the MVP algorithm uses user perceptual video quality rather than video bitrate to reduce the bandwidth demand between viewpoints. Consequently, the bandwidth can be distributed efficiently for all viewpoints. Combined with dynamic quality target adjustment and segment redownloading, the performance of the MVP algorithm is further improved. However, the MVP algorithm requires a well-defined configuration to achieve the best performance. Hence, we also propose a deep reinforcement learning strategy called DRLMVP, which adaptively learns the best quality combination without any viewpoint prediction. Based on the evaluation conducted on the NS3 simulator, the proposed algorithm outperforms another method with improvement over MV-QoE performance.