A frequency offset estimation and correction method in an orthogonal frequency division multiplexing (OFDM) system is disclosed in present invention, including: obtaining a pilot frequency domain channel estimation value of a target user, and smoothing the channel estimation value in frequency domain; obtaining the link quality state of a receiver; adopting a history smoothing algorithm or a multi-branch attempt algorithm to perform frequency offset estimation and frequency offset compensation, performing frequency domain demodulation for the data for which frequency offset compensation has been performed, and outputting a link quality state parameter; and updating the link quality state of the receiver according to the link quality state parameter, determining the output value of this frequency offset estimation and outputting a history frequency offset value required by next frequency offset estimation according to the determined output value of this frequency offset estimation. A corresponding apparatus is also disclosed in the present invention.