Aiming at the problem that the desired response error of the least mean square (LMS) adaptive filter constructed by spectral subtraction and spectrum method was large under the condition of low signal-to-noise ratio (SNR), based on the analysis of LMS adaptive filtering principle, an autocorrelation method is proposed to construct the desired response of LMS adaptive filter. Firstly, according to the characteristic that the noise was uncorrelated at different times, the input signal was delayed; then, in order to detect the periodic signal from the low signal-to-noise ratio environment, the autocorrelation of the delayed signal was calculated; finally, the autocorrelation signal was taken as the expected response. Simulation results show that the proposed method is effective and can accurately construct the desired response for LMS adaptive filtering under the condition of low SNR.