Abstract: The spectral components of speech are usually assumed to be independent in traditional short-time spectrum estimation, which is not the case in practice. To solve this problem, a new speech enhancement algorithm with multivariate Laplace speech model is proposed in this paper. Firstly, the speech Discrete Cosine Transform (DCT) coefficients are modeled by a multivariate Laplace distribution, so the correlations between speech spectral components can be exploited. And then a Minimum-Mean-Square-Error (MMSE) estimator based on the proposed model is derived using a Gaussian scale mixture representation of random vectors. Furthermore, the speech presence uncertainty with the new model is derived to modify the MMSE estimator. Experimental results show that the developed method has better noise suppression performance and lower speech distortion compared to the traditional speech enhancement method.