In the copper electro-refining process, short circuiting between the cathode and anode caused by nodulation has the largest impact on the loss of current efficiency. In order to improve current efficiency, it is critically important to study the mechanism of the growth of the nodule. In this study, the nodulation was modeled using the finite element method to simulate the growth of copper bumps attached to the cathode. By considering the scale of the electrodes and their pitch, the relationship between the height of the nodule and its growth rate is investigated. In particular, a threshold height of the nodule that determines whether the nodule will rapidly grow to come in contact with the adjacent anode is identified. By comparing the result of the simulation and the experiments, the effect of leveling additives and the generation of dendritic growth are discussed.