There are few works on the problem of heavy noise corruption in wavelet-based speech enhancement. In this paper, a new method is introduced to adapt the weighting function for wavelet coefficients (WCs) in each subband. The idea is based on that the change of WC variance in speech-dominated frames is larger than the change of WC variance in noise-dominated frames. We can define a weighting function for WCs in each subband so that WCs are preserved in speech-dominated frames and reduced in noise-dominated frames. Then a weighting function in terms of WC's variance is derived. The experimental results show that the proposed method is more robust than that of SNR adjusted speech enhancement system.