‎The class of α-stable distributions incorporates both heavy tails and skewness and so are the most widely used class of distributions in several fields of study which incorporates both the skewness and heavy tails‎. ‎Unfortunately‎, ‎there is no closed-form expression for the density function of almost all of the members of this class‎, ‎and so finding the maximum likelihood estimator for the parameters of this distribution is a challenging problem‎. ‎In this paper‎, ‎in order to tackle this issue‎, ‎we propose some type of EM algorithm‎. ‎The performance of the proposed EM algorithm is demonstrated via simulation and analyzing three sets of real data‎.