In this paper, we deal with the consensus algorithm proposed by Kamon & Ohki in the case of networked N-dimensional quantum systems, and show several basic results which give a direction for the complete proof of its global stability. In particular, a candidate of Lyapunov functions for the consensus problem is proposed and it is shown that the algorithm makes all of the quantum states converge to a certain subset including the consensus states. We also justify our approach by using numerical simulations.