This paper presents an efficient adaptive predistortion technique compensating linear and nonlinear distortions caused by high-power amplifier (HPA) with memory in OFDM systems. The efficient adaptive data predistortion techniques proposed for compensation of HPA with memory in single carrier systems cannot be applied to OFDM systems since the possible input levels for HPA is infinite in OFDM systems. Also, previous adaptive predistortion techniques, based on Volterra series modeling, are not suitable for real-time implementation due to high computational burden and slow convergence rate. In the proposed approach, the memoryless HPA preceded by a linear filter in OFDM systems is modeled by the Wiener system which is then precompensated by the proposed adaptive predistorter with a minimum number of filter taps. An adaptive algorithm for adjusting the proposed adaptive predistorter is derived using the stochastic gradient method. It is demonstrated by computer simulation that the performance of OFDM system suffering from nonlinear distortion can be greatly improved by the proposed efficient adaptive predistorter using a small number of filter taps.