Adaptive predistorter is an effective technique to compensate for nonlinear distortion in a power amplifier. As a method to improve the parameter convergence speed in the predistorter, a series expansion technique with an orthogonal polynomials has been investigated. In this paper, we present an adaptive predistortion linearization method based on orthogonal polynomial expansion for a nonlinear power amplifier affected by memory effect in OFDM systems, where both memory and memoryless predistorter are constructed by the weighted sum of orthogonal polynomials. In addition, to achieve the parameter optimization speed improvement of the predistorter, we propose a method to determine step-size in a recursive calculation. The parameter convergence performance of the predistorter is investigated in OFDM systems with and without peak-to-average power ratio (PAPR) reduction, where the partial transmit sequence (PTS) technique is employed to reduce PAPR. Computer simulation results show that the proposed adaptive predistorter achieves faster parameter convergence time than that of non-orthogonal one in OFDM systems with nonlinear power amplifier affected by memory effect, even though PAPR of OFDM signal is reduced by using PTS. It is also confirmed that power added efficiency is further improved by combining the adaptive predistortion with PAPR reduction technique.