OFDM(Orthogonal Frequency Division Multiplexing) signals sutler serious nonlinear distortion in the nonlinear HPA(High Power Amplifier) because of high PAPR(Peak Average Power Ratio). Nonlinear distortion can be improved by a pre-distorter, but this pre-distorter is insufficient when the PAPR is very high in an OPFDM system. In this paper, a DFT(Discrete Fourier Transform) transform technique is introduced for PAPR reduction. It is especially important to consider the memory effect of HPA for more precise predistortion. Therefore, in this paper, we consider two models, the TWTA(Traveling-Wave Tube Amplifier) model of Saleh without a memory effect and the HPA memory polynomial model that has a memory effect. We design a pre-distorter and an adaptive pre-distorter that uses the NLMS(Normalized Least Mean Square) algorithm for the compensation of this nonlinear distortion. Without the consideration of a memory effect, the system performance would be degraded, even if the pre-distorter is used for the compensation of the nonlinear distortion. From the simulation results, we can confirm that the proposed system shows an improvement in performance.