Two dimensional nucleation process on substrate is investigated by Monte Carlo simulation, and the critical nucleus size and its waiting time are measured with a high accuracy. In order to measure the critical nucleus with a high accuracy, we calculate the attachment and the detachment rate to the nucleus directly, and define the critical nucleus size when both rate are equal. Using the kinematical nucleation theory by Nishioka, it is found that, our obtained kinematical two dimensional critical nucleus size are about ten percent smaller than the thermodynamically defined one. The dependence on the chemical potentials for the critical nucleus size is good agreement with the classical nucleation theory. For the surface diffusion dependence of the critical nucleus size, it is found that the critical nucleus size increases as the surface diffusion length to long distance
