Dynamic adaptive streaming over HTTP (DASH) has been widely deployed. However, large latency in HTTP/1.1 cannot meet the requirements of live streaming. Data - pushing in HTTP/2 is emerging as a promising technology. For video live over HTTP/2, new challenges arise due to both low-delay and small buffer constraints. In this paper, we study the rate adap-tion problem over HTTP/2 with the aim to improve the quality of experience (QoE) of live streaming. To track the dynamic characteristics of the streaming system, a Markov-theoretical approach is employed. System variables are taken into ac-count to describe the system state, by which the system transi-tion probability is derived. Moreover, we design a dynamic re-ward function considering both the quality of user experience and dynamic system variables. Therefore, the rate adaption problem is formulated into a Markov decision based optimiza-tion problem and the best streaming policy is obtained. At last, the effectiveness of our proposed rate adaption scheme is demonstrated by numerous experiment results.