Generalized distributions have been studied a lot recently because of their flexibility and relia-bility in modeling lifetime data. The two-parameter exponentially-modified logistic distribution is a new flexible modified distribution that was introduced recently. It is regarded as a strong competitor for widely used classical symmetrical and non-symmetrical distributions such as normal, logistic, lognormal, and log-logistic. In this study, the unknown parameters of the dis-tribution are estimated using the maximum likelihood method. The Grey Wolf Optimization al-gorithm, which is a new meta-heuristic algorithm, is applied in order to solve the nonlinear like-lihood equations of the study model. The performance of the Grey Wolf Optimization method is compared to that of the other meta-heuristic algorithms used in this study, which include the Whale Optimization Algorithm, the Sine Cosine Algorithm, and the Particle Swarm Optimiza-tion Algorithm. The efficiencies of maximum likelihood estimates for all algorithms are com-pared via an extensive Monte-Carlo simulation study. The likelihood estimates for the location α and scale β parameters of the exponentially-modified logistic distribution developed with the Grey Wolf Optimization algorithm are the most efficient among others, according to simulation findings. Four real datasets are analyzed to show the flexibility of this distribution.