Abstarct: The name " speech enhancement '' refers to larg group of methods that improve the quality and intelligibility of noisy speech by suppressing the background noise from noisy signal. There are a lot of methods and papers about speech enhancement, but estimation of the clean signal from the noisy signal is still one of the insoluble problem in speech processing field . One of the most important methods for speech enhancement, are statistical methods, because they have better performance. In these methods, a distribution for clean speech and noise are assumed. Then an estimator are used for estimating the clean signal from noisy signal. In this thesis, an estimator for speech enhancement in Discrete Fourier Transform (DFT) domain is proposed. It is shown that the complex DFT coefficients of clean speech can be modeled more accurate, by Laplacian Mixture Model than Gaussian, Laplacian and GMM distributions. Then, an analytical solution for estimating the complex DFT coefficients with the MMSE (Minimum Mean Square Error) estimator is derived, when the clean speech DFT coefficients are mixture of Laplacians distributed and the DFT coefficients of noise are Gaussian distributed. The derived MMSE estimator is non-linear and it is shown that, this estimator has better performance than the estimators which are baxsed on Laplacian or Gaussian models. For estimating LMM's parameter the Expectation Maximization (EM) Algorithm is used. Indeed, the parameters of LMM are estimated offline with clean speech from TIMIT data baxse and the parameters of noise are estimated online with minimal tracking baxsed method. Finally, the proposed algorithm is evaluated in term of Segmental SNR, LLR(Log Likellihood Ratio) and PESQ (Perceptual Evaluation Of Speech Quality) and then the proposed method is compared with Laplacian and Gaussian baxsed methods. The results of this comparison shows that the proposed method has an acceptable performance.