The predistorter is commonly used for the nonlinearity compensation of high power amplifier (HPA), a device in many communication systems whose inherent nonlinearity causes in-band and out-of-band distortion. In order to reduce the implementation complexity and computational load, the static (or memory-less) polynomial model based predistorters are extensively employed due to its simplicity. However, in fact, as shown in this paper, a static rational function (RF) model with almost equivalent complexity to the polynomial model, can provide a more accurate compensation. By investigating the mean-square-error (MSE) of residuals by least-square estimation in detail, theoretically we find that the rational functional model with the same order in the numerators as that of polynomial model always gives a smaller MSE. Furthermore, it is indicated by simulation, that a lower order rational function model can give better compensation effect than a higher order polynomial model in most cases. Based on these analysis, an adaptive RF predistorter (RF-PD) is developed for the nonlinearity compensation of high power amplifier. The simulation results verified the efficiency of the proposed method.