This paper discusses the effect of frequency offset on the performance of OFDM communications systems. The most important requirement in an OFDM is frequency and time synchronization as this form the reason for orthogonality between the subcarriers. However OFDM is susceptible to synchronization errors between transmitter and receiver local oscillator frequencies. This error is known as the carrier frequency offset (CFO) [1] and causes ICI and it also destroys the orthogonality between the subcarriers that¿s why performance of OFDM systems is degraded by the Carrier Frequency Offset (CFO) . In this paper we study the effects that CFO can cause to the SNR in an OFDM system, and estimate the amount of frequency offset.