HTTP Adaptive Streaming (HAS) has become a popular solution for media delivery over the mobile Internet. However, existing HAS systems are based on the pull-based HTTP/1.1 protocol, leading to high overheads (e.g., in terms of energy, processing, bandwidth) for clients, servers, as well as network nodes. The new HTTP/2 protocol provides a server push feature, which allows the client to receive more than one video segment for each request in order to reduce request-related overheads. In this study, we propose an adaptation method to leverage the push feature of HTTP/2. Our method takes into account not only the request-related overhead but also buffer stability and gradual transitions. The experimental results show that our proposed method performs well under strong throughput variations of mobile networks.