The frequency offset estimation is used to correct any frequency error of the local reference oscillator. In this letter, a frequency offset estimation algorithm utilizing the peak phase error detection and frequency offset smoother is proposed for burst data transmission. The basic idea of frequency offset estimator is to use a curve fitting method. The proposed peak phase error detection avoids a large phase error which yields a bad value for FOE. In order to control the AFC, frequency offset smoother by a simple filter is used. Simulation results show that the proposed algorithm is adequate for frequency offset estimation of burst data transmission.