Provided is an apparatus for estimating a frequency offset by one training symbol including two symbols having the same structure and value in an OFDM system. The apparatus includes a first likelihood function calculator for modeling non-Gaussian impulsive noise included in the training symbol to a Cauchy probability density function in which a characteristic exponent of a BISαS probability density function is 1, and calculating a likelihood function of a Cauchy distribution using the Cauchy probability density function, and a first frequency offset estimator for estimating an effective frequency offset value in which the likelihood function of the Cauchy distribution of the first likelihood function calculator becomes highest as a frequency offset estimation value. Thereby, it is possible to improve the performance of frequency offset estimation in non-Gaussian impulsive noise environments.