The continuing advances in the storage and transmission abilities of user equipment have made it possible to share videos through device-to-device communications, which may be an efficient way to enhance the capacity of cellular network to provide wireless video services. In adaptive D2D video streaming, user experience is greatly influenced by the quality and fluency of the video, which is affected by the D2D link's quality. Additionally, the quality of D2D links relies on the resource allocation scheme for D2D pairs. To improve the quality of experience in D2D video streaming, we propose a QoE-aware resource allocation scheme for adaptive D2D video streaming. The QoE-aware resource allocation scheme has the ability to cater to the user experience in adaptive video steaming while considering the co-channel interference derived from frequency reuse in D2D communications. Specifically, a dynamic network scheduling problem is formulated and solved, with the objective of maximizing the video quality while maintaining the long-term stable performance of fluency during video playback. Extensive numerical results demonstrate that the proposed QoE-aware resource allocation scheme outperforms the QoE-oblivious resource allocation scheme.