At present, there are difficulties in the governance of Internet rumors, such as slow control and information barriers. In the face of the confused and complex social public opinion environment, it is urgent to innovate technical means to break through the bottleneck of rumor prevention and control. Firstly, based on the architecture characteristics and core technologies of blockchain, this paper designs a multi-blockchain system architecture for the collaborative co-governance scenario of online rumors, and puts forward the design ideas of smart contracts and consensus mechanisms for the functions of different chains, so as to enable different chains and different nodes within each chain to achieve collaborative interaction of rumor dispelling and rumor suppression strategies. Secondly, according to the requirements of the rumor co-governance scenario, we improve the original PBFT consensus algorithm on the basis of analyzing the defects, and propose the RK-PBFT consensus mechanism based on rumor refutation reliability and K-Medoids clustering algorithm. Through the simulation experiment, the algorithm is compared before and after the improvement. The results show that the delay of the proposed improved consensus algorithm is significantly reduced and the throughput is greatly improved, in addition, in the case of the same number of nodes, the more the number of packets, the lower the delay and the higher the throughput. This means that the proposed consensus algorithm not only improves the delay and throughput performance of the original algorithm, but also ensures the reliability and operation efficiency of the rumor co-governance system.