In this paper, a fast and high-efficiency carrier frequency offsets (CFO) estimation algorithm is proposed. This new algorithm exploits the intrinsic structure information of OFDM signals and the unimodality of the cost function for CFO estimation. It reduces the computational complexity by using the golden section method in searching for the extremum of the cost function. The performance of the proposed algorithm is investigated with numerical simulations. The results show that the new algorithm has much lower complexity than Turelis MUSIC-like approach while achieves same performance in both additive white Gaussian noise (AWGN) and multipath fading channels.