With the growing development of wireless communications systems, the use of systems with high data rates has arrested attention that can be noted to OFDM systems among these systems. The important features of this system are efficient usage of bandwidth and resistance to errors caused by the multipath propagation environment. OFDM systems have a high sensitivity to frequency offset. Due to the importance of signal eavesdropping in the cyber defence, in order to compensate frequency offset, it is necessary to use blind frequency estimation methods based on the inherent structure of the system and without the use of pilot symbols. Accordingly, in this paper, a blind frequency offset estimation algorithm based on cyclic prefix (CP) by using adaptive algorithms is presented that is closed to the optimum frequency offset during a step by step algorithm. In the proposed method, the Normalized Least Mean Square (NLMS) and Recursive least squares (RLS) adaptive algorithms are used to provide a method for estimating the frequency offset. The main feature of the new presented method is the ability to estimating the frequency offset in the presence of the time offset and in multipath channel with frequency-selective fading. According to the simulations results that are performed in the frequency-selective fading channel, MSE criterion in the NLMS proposed method about 3 dB and in the RLS proposed method approximately 7 dB has improved compared to other methods.