In the rumor propagation model, different people have different attitudes towards a rumor. This article considers the four attitudes of different people to rumors: unknown (S), hesitation (H), spread (I), and resistance (R)’s rumor spreading model, on this basis, considers impulsive supervision by the government. Under impulsive intervention, that is, the government’s role in refuting rumors, both hesitating and disseminating will tend to zero, and the number of people resisting rumors will increase and tend to increase rapidly. It is stable, and the rate of increase of resisters is proportional to the correlation coefficient p of impulse supervision. The numerical simulation results have taken different p values, and the conclusions drawn also well confirm that the larger the p value, the speed of the increase of resisters is also Faster.