We introduce a measurement method for measuring the chemical potential of gold nanoclusters, which are bound to Au(111) substrate through tunneling barrier, by using scanning tunneling spectroscopy. Tunneling spectra show Coulomb staircase, by which the chemical potential of nanoclusters can be determined. The statistical analysis is performed on the position of the chemical potential of the nanoclusters relative to the Fermi level of the substrate. We found that the chemical potential of gold nanoclusters distributes around the Fermi level of the substrate and the standard deviation depends on the size of clusters. This size dependence of the deviation clearly shows the process of the charge neutrality breakdown of clusters.