Summary: The spread of rumors not only causes massive economic losses, but also seriously threatens social harmony and stability of human livelihoods. As a result, preventing rumors from spreading is critical. Individuals’ familiarity with rumors and refuters has a significant impact on their spread. We develop a rumor propagation model that introduces familiar mechanisms and refuters, as well as demonstrating the existence of an equilibrium point and its local and global asymptotic stability in the model. We also calculate the model’s basic regeneration number. Subsequently, we select two appropriate control variables: the contact rate between the ignorant, who are familiar with the rumor, and the disseminators; and the probability that the disseminators will become refuters. We discover that the control effect is optimal when the first variable is minimum and the second variable is maximum. Numerical simulation verifies the accuracy of the obtained results, and sensitivity analysis of the parameters is investigated. According to the research, an increase in the proportion of disseminators who become refuters will slow the spread of rumors, while an increase in the population of ignorant people who are familiar with rumors contacting the disseminators will accelerate the spread of rumors.