In an attempt to find a novel catalyst system for atom transfer radical polymerization (ATRP), a parameter estimation method based on nonlinear regression was developed to evaluate various catalyst systems by determining kinetic parameters of polymerization. From our model system considering small molecular atom transfer addition reaction, we found that equilibrium constant of atom transfer reaction could be successfully determined using our parameter estimation method. However, the each value of activation rate constant and deactivation reaction constant is hard to be determined ubiquitously because of the poor sensitivities of them and the local minima trapping. By applying second minimization algorithm, the parameter estimation algorithm achieves higher propensity to reach global minimum, yet not all the time. The simulation results using kinetic rate constants determined by our method shows better agreement with the experimental data than that using literature values. This is because the current method uses fewer assumptions than other literature methods in determining rate constants. We also demonstrated the determination of kinetic constants in the polymerization of styrene and MMA using various metal catalysts, and the simulations using these kinetic constants agree well with the experimental data.