This paper addresses the problem of speech enhancement in wavelet domain. After decomposition of noisy signal into wavelet sub-bands, an adaptive thresholding process is applied on wavelet coefficients. In the proposed technique, small threshold value and hard thrsholding function are used in sub-bands with high speech energy; vice versa, in sub-bands with low speech energy, large threshold value and soft thresholding function are employed. For other sub-bands (between above two extreme cases for speech energy), we use an adaptive thresholding function that is actually between soft- and hard-thresholding functions. The threshold value and thresholding function are determined by a parameter related to the ratio of speech and noise powers in each sub-band. Our extensive experiments show the superiority of proposed method in removing the background noise and reduction of speech distortion. It was also shown that both wavelet tree structure and wavelet type affect on the performance of speech de-noising system.