In this paper, an efficient blind carrier frequency offset (CFO) estimation method in orthogonal frequency division multiplexing (OFDM) systems is proposed. In the proposed method, we obtain two time different received OFDM symbols by using both the cyclic prefix and oversampling technique, and a cost function is defined by using the two OFDM symbols. We show that the cost function can be approximately expressed as a cosine function. Using a property of the cosine function, a formular for estimating the CFO is derived. The estimator of the CFO requires three independent cost function values calculated at three different points of frequency offset. The proposed method is very efficient in computational complexity since no searching operation for the minimum cost value is required. The proposed method reduces 97% of the amount of FFT computation, compared with the ML method. Unlike the conventional methods such as the ML method and the 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 ML method.