Abstract: The truth-telling people can spread the true facts and refute the rumor. A rumor spreading model integrated with this truth-telling mechanism is developed on homogeneous networks. The mean field equations are derived accordingly, and the stability analysis is conducted as well. The numerical analysis is carried out on a real social network, Livejournal to investigate the impacts of the truth-telling mechanism on the rumor spreading. The results show that when the system goes steady, there are only stiflers and truth-tellers left; the truth-telling mechanism hampers the diffusion speed of the rumor and cuts down the final size of the rumor; the effects of the network structure change with the parameters in the truth-telling mechanism, i.e. when the truth spreading rate stays relatively high, the BA scale-free network has a larger final size of the rumor than the regular network, while in other cases, the final size of the rumor on regular network is larger than that on the BA scale-free network.