Maximum likelihood (ML) is an optimal parameter estimation technique. When applying this technique to the problem of modulation sequence estimation, it is found that the resulting estimate is unpractical due to the unavailability of an efficient way to perform the required maximization. The expectation-maximization (EM) algorithm is a statistical mean that can provide maximum likelihood parameter estimation. In this paper, this algorithm is applied to the problem of estimation of the modulation sequence of M-ary Phase Shift Keying (MPSK) signals contaminated with additive white Gaussian noise and traveled over Rayleigh fading channel. The algorithm obtains a suitable iterative mean for computing ML estimate of the sequence and performs the task that has been previously too complex to perform. Simulation experiment is performed to validate the theoretical developments and to measure the performance of the algorithm. The performance of the algorithm is measured in terms of the symbol error probability.