Social networks have been developed into one of the most important media for rumor fermentation and propagation, and it is necessary to disclose how the rumor spreads in social networks.Combined with the imports of spatial temporal delay, spatial diffusion and media coverage,a new delayed reaction diffusion rumor spreading model is developed. Applying the theory of partial functional differential equation, some stability and Hopf bifurcation conditions are given for the model. Examples are given to validate that delay can influence the convergence rate and the stability of the model, and media coverage benefits to reduce the density of rumor spreaders and expands the stability domain. Finally, some useful strategies forrumor spreading control in social networks are presented.