An algorithm for estimation of the amplitudes and phases of composite Continuous Wave (CW) signals is considered. The signals are contaminated with non-Gaussian noise. The considered noise model is the most commonly exist in communication applications. The developed algorithm for estimating the amplitudes and phases of composite CW signals is based on the Expectation Maximization (EM) algorithm. The most feature of the developed algorithm is that it reduces the complicated multiparameters optimization required when using the ML approach. The complexity of the algorithm is essentially unaffected by increasing the number of composite signals. Simulation experiment is performed to illustrate the performance of the developed algorithm.