Aiming at the problem that spreader nodes will be influenced by their neighbors during the recovery in the rumor propagation process, a rumor propagation model based on edge-based compartmental theory was proposed. Firstly, a set of dynamic equations were established using the improved edge-based compartmental theory, and the propagation range and breaking threshold were theoretically analyzed. Then the influence of factors including network structure, propagation probability and basic recovery probability were analyzed through numerical simulation. Finally, an effective immunization strategy to control rumor propagation range and breaking threshold was presented on the above basis. The results of theoretical analysis and numerical simulation show that, compared with the classical SIR (Susceptible-Infected-Recovered) rumor propagation model, the presented model decrease the period of rumor propagation and increase the peak of the propagation of spreader nodes slightly. Through comparison experiments with the random immunization strategy, in the proposed strategy the edges with higher product of the degrees of two nodes were immuned preferentially to obtain better effect when rumor has minor propagation probability, and the edges with lower product of the degrees of two nodes were immuned preferentially to obtain better effect when rumor has larger propagation probability. Study results indicate that the presented model conform to the characteristics of rumor fading away phase and can provide theoretical and numerical support for rumor prediction and control.