This paper proposes an efficient blind deterministic carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM) systems. In the proposed method, two OFDM symbols with time difference are generated by exploiting both the oversampled OFDM signal and the cyclic prefix, and a cost function is introduced for CFO estimation. It is shown that the cost function can be expressed as a cosine function. Using a property of the cosine function, a formula for deterministically estimating the CFO is derived. The proposed method is very suitable for real wireless environments since it requires only one OFDM symbol for blind reliable estimation of CFO. The proposed method is very efficient in computational complexity since no searching operation for the minimum cost value is required. The computer simulations show that the performance of the proposed method is superior to those of the MUSIC method  and the ML method .