In this paper, the relation of the moving consensus of multi-agent systems and the power-law characteristic of the scale-free network is studied. Firstly, a consensus-preference scale-free network (CPSF network) model, which has the variable power-law parameters, is presented on the network reconstructed mechanism. Then, the effects of the power-law on the consensus of the multi-agent systems are analysed by adjusting the constructed parameters to change the algebraic connectivity of the scale-free networks. Finally, the converging speeds of multi-agent systems on scale-free network with different configuration are studied by many computer simulations.