Measurement noise may have an important impact on the collective motion. Here, we investigate the consensus problem of multiagent networks with multiplicative measurement noise. Based on the stability theory of stochastic differential equations and the algebra graph theory, we obtain sufficient conditions for the consensus and nonconsensus. Both of our analytical and numerical results show that the multiplicative measurement noise can facilitate the emergence of the consensus: the convergence rate increases with respect to the noise intensity if the topologies of the underlying networks satisfy some conditions. Our results provide a better understanding of the constructive role of noise. We also report that the convergence rate of multiagent networks is strongly affected by the network topology and the group size.