This paper presents an efficient adaptive predistortion technique compensating for nonlinear distortions caused by a high-power amplifier (HPA) cascaded with a linear filter in an OFDM system. In the proposed approach, the memoryless HPA, preceded by a linear filter with memory 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. It is confirmed by computer simulation that the proposed approach produces a faster convergence speed than the previous adaptive predistortion technique, and provides a small output backoff as low as 5.5 dB for an OFDM system employing an HPA with a linear filter.