In this paper, we propose a new adaptation approach for viewport-adaptive streaming of 360-degree videos over the Internet. The proposed approach is able to systematically decide quality levels of tiles according to user head movements and network conditions by taking into account not only prediction errors but also user head movements in each adaptation interval. Experimental results show that the proposed approach can effectively adapt 360-degree videos to both varying network conditions and user head movements. Compared to existing approaches, the proposed approach can improve the average viewport quality by up to 3.9dB and reduce the standard deviation of the viewport quality by up to 50%.