Recently, Dynamic Adaptive Streaming over HTTP (DASH) has become popular for video delivery in multimedia network. However, HTTP streaming is currently based on the pull-based HTTP/1.1 protocol which requires a large number of client requests for each streaming session. Moreover, most of adaptive streaming methods have just focused on the case of CBR (constant bitrate) video. In this paper, we introduce a new method for quality adaptation of VBR (variable bitrate) videos in on-demand streaming over the new HTTP/2 protocol using server push feature. To the best of our knowledge, this is the first study on streaming VBR videos over HTTP/2. Experimental results show that the proposed method can provide a lower number of requests, a higher average quality and more smooth video quality than existing methods.