Summary: The relations of the network topology and the moving consensus of multi-agent systems are studied. A consensus-prestissimo scale-free network model with the static preferential-consensus attachment is presented on the rewired link of the regular network. The effects of the static preferential-consensus BA network on the algebraic connectivity of the topology graph are compared with the regular network. The robustness gain to delay is analyzed for variable network topology with the same scale. The time to reach the consensus is studied for the dynamic network with and without communication delays. By applying the computer simulations, it is validated that the speed of the convergence of multi-agent systems can be greatly improved in the preferential-consensus BA network model with different configuration.