Copper electroplating is widely used for fabrications of Large-Scale Integration (LSI) besides other methods such as sputtering because of its excellent via/trench filling ability, good adhesion and lower process temperature and low cost. In the electroplating process, real-time estimating a growth rate of electroplating is essential. It is possible to estimate the growth rate of electroplating from the current density on the LSI wafer surface because the rate is mainly proportional to the current density. In this paper, a new monitoring method to estimate the LSI plating current density distribution from electric potentials in the plating bath is developed. The proposed method measures electric potentials at several points in the bath using capillaries, and estimates the current density on the LSI wafer surface by applying an inverse analysis method. In the inverse analysis, an observation equation is modeled by considering that the electric potentials in the bath obey the Laplace equation, which is solved by Bayesian estimation. In order to demonstrate the effectiveness of the proposed method, numerical simulations which involve measurement errors are performed for a sample polarization curve of Cu in CuSO4. The results show that this method could be applied to practical problems. In addition, using a priori information for the possible shape of the polarization curve, the estimate accuracy of the proposed method is shown to be improved.