In order to overcome the impact of inter-symbol interference under multipath channels, The channel estimation and equalization algorithm in the SC-FDE system are studied in the paper. The principle of DFT interpolation algorithm is analyzed, and a method of using Golay sequence to estimate the channel frequency response is proposed, then the MMSE equalization estimation parameters are derived in detail. Finally, the time domain filtering in the equalization algorithm is simulated and verified by Matlab, the results show that the method can filter out noise to a limited extent and improve the system receiving performance under multipath channels, and has certain application value.