Abstract: Multitaper spectrum has lower variance than the traditional periodogram. The noise spectrum and the Noise to Noisy Signal Ratio (NNSR) are estimated from the multitaper spectrum of the noisy signal; the pre-enhanced speech for calculating the noise masking threshold is obtained by the spectral amplitude subtraction method, whose gain is a function of NNSR; the final enhanced speech is obtained by suppressing the Fourier spectrum of the noisy signal with the psychoacoustical weighting rule incorporating the noise masking threshold. Because of the low variance feature of the multitaper spectrum, a modified offset formula is proposed to calculate the noise masking threshold, thus the reconstructed speech with this modification has an improvement in MBSD (Modified Bark Spectral Distortion). When a maximum limitation less than one to the psychoacoustical weighting rule is further proposed, the higher the input SNR (>0 dB) is, the more improvement the segmental SNR and the overall SNR have. The informal listening tests show that there is little speech distortion for the enhanced speech processed by the proposed method, the background noise is reduced much and free of musical noise.