In this paper, we focus on three different polynomial formats used in power amplifiers (PAs) pre-distortions. The nonlinearity of AM/AM and AM/PM introduced by power amplifiers are revealed by the transfer characteristics of PAs. We pick out the most effective polynomial format in evaluation of relative MSE (RMSE), the convergence speeds and the power spectral density (PSD). Such effective polynomial format is of great importance in PAs pre-distortion based on polynomial methods, in which the pre-distortion can be made more stable. The above mentioned aspects are all demonstrated through computer simulations and corresponding analysis.