The OFDM system is characterized by the Gaussian - like signal behavior with a relatively high peak-to-average power ratio (PAPR). As a result, the performance of OFDM system is very sensitive to nonlinear distortions, which arise mainly from the high power amplifier (HPA). In addition, the wideband characteristics of transmitted signals cause the nonlinear distortions to be frequency - dependent. This paper proposes an identification-based adaptive pre-distortion scheme, which is constructed by using the indirect learning architecture, to compensate nonlinearity of the HPA with memory effects. Simulation results show that the proposed adaptive pre-distortion scheme can effectively suppress spectral re-growth and reduce in - band distortion for HPA with memory.