In view of the fact that the study of the positive ideology propagation rarely takes into account of the dynamic model, we built the positive ideology propagation model based on forgetting mechanism. By using the Hurwitz criterion, Lyapunov stability theorem and LaSalle invariance principle, the local stability and global stability of the equilibrium points of ideology propagation were analyzed. The relationship between the propagation threshold and forgetting/cotact rate of influence factors of ideology propagation was obtained. The simulation results show that the range of ideology propagation will be expanded when the rate of forgetting reduces or the contact rate increases. That is to say, the spread range is negatively correlated with the forgetting rate and positively correlated with the contact rate, respectively.