The Hypertext Transfer Protocol (HTTP) has been widely adopted and deployed as the key protocol for video streaming over the Internet. One of the consequences of leveraging traditional HTTP for video streaming is the significantly increased request overhead due to the segmentation of the video content into HTTP resources. The overhead becomes even more significant when non-multiplexed video and audio segments are deployed. In this paper, we investigate and address the request overhead problem by employing the server push technology in the new HTTP 2.0 protocol. In particular, we develop a set of push strategies that actively deliver video and audio content from the HTTP server without requiring a request for each individual segment. We evaluate our approach in a Dynamic Adaptive Streaming over HTTP (DASH) streaming system. We show that the request overhead can be significantly reduced by using our push strategies. Also, we validate that the server push based approach is compatible with the existing HTTP streaming features, such as adaptive bitrate switching.