A method is proposed for estimating the source signal and its direction of arrival (DOA) in this paper. It is based on ML estimation of the transfer function between microphones combined with the EM algorithm for a Gaussian Mixture Model (GMM), assuming that the signal is captured at each microphone with delay corresponding to the traveling of sound and some decay. By this modeling, search for the maximum log-likelihood in the ML estimation can be realized simply by eigenvalue decomposition of a properly designed matrix. Computer simulation results show that the proposed method achieves SDR of greater than 10 dB regardless of amplitude difference between microphones and DOA estimation error of less than 8 degrees, on average. It is also shown that it can maintain high performance in various conditions.