Abstract: In general, some methods of blind signal processing ignore noise, but in practice, noise affects the performance of algorithms, especially seriously in some areas. This paper provides solutions to the problem that mixing matrix is estimated blindly in Gaussian noise with unknown covariance. Based on Maximum Likelihood estimation, the equations are given for solving the mixing matrix and covariance matrix. Gaussian Mixture Model (GMM) is used to approximate the pdf of sources and results in a practical Expectation Maximum (EM) algorithm. Computer simulation shows that this algorithm is convergent and has good performance in low SNR.