When a rumor appears on social networks, the media of relevant departments need reaction time to make an authoritative announcement. Considering the effects of the media report and time delay on a rumor spreading, and the different attitudes of individuals towards media reports. We proposed a susceptible-expose-infective-media-remover (SEIMR) rumor propagation model with media reports and time delay. Firstly, the basic reproduction number of the model is obtained. Secondly, the positivity, boundedness and existence of the solutions of the model are analyzed. Then, the local asymptotic stability of the rumor free equilibrium and the boundary equilibriums is proved, and the global asymptotic stability of the equilibriums is proved by constructing Lyapunov function when the time delay is zero. Besides, the prevention and control effects of the media report on rumor spreading and the effect of time delay are analyzed. The shorter time delay in media report and the greater the impact of the media report, the more effective the suppression of rumors will be. Finally, the accuracy of the theoretical results as well as the effects of different parameters of the model have been verified through numerical simulations, and the effectiveness of the SEIMR model has been verified via comparative experiments.