360-degree video delivery in Virtual Reality is very challenging due to the fact that 360-degree videos require much higher bandwidth than conventional videos. To overcome this problem, viewport-adaptive streaming has been introduced. In this study, we propose a new adaptation method for tiling-based viewport-adaptive streaming of 360-degree videos. For content preparation, the Cubemap projection format is used, where faces or parts of a face are encoded as tiles. Also, the problem is formulated as an optimization problem, in which each visible tile is weighted based on how that tile overlaps with the viewport. To solve the problem, an approximation algorithm is proposed in this study. An evaluation of the proposed method and reference methods is carried out under different tiling schemes and bandwidths. Experiments show that the Cubemap format with tiling provides a lot of benefits in terms of storage, viewport quality across different viewing directions and bandwidths, and tolerance to prediction errors.