In this paper, an efficient blind frequency offset estimation method for radio resource saving in orthogonal frequency division multiplexing (OFDM) systems is proposed. In the proposed method, we obtain two time different received OFDM signal blocks by using the cyclic prefix and define the cost function by using the two OFDM signal blocks. We show that the cost function can be approximately expressed as a closed form cosine function. The approximated cosine function can be obtained from three independent cost function values calculated at three different frequency offsets. In the proposed method, the frequency offset can be estimated by calculating a frequency offset minimizing the approximated cosine function without searching all the frequency offset range. Unlike the conventional methods such as MUSIC method, the accuracy of the proposed method is independent of the searching resolution since the closed form solution exists. The computer simulation shows that the performance of the proposed method is superior to those of the MUSIC and the oversampling method.