In this paper, we discuss the problem of estimating the parameters for the Gompertz distribution in the presence of outliers. The maximum likelihood (ML) method is used to estimate the unknown parameters for Gompertz distribution in the presence of outliers. Simulation study and real data analysis are conducted in the presence of outliers. A simulation study is presented to discuss the behavior of ML estimators. The performance of the ML estimates for the Gompertz distribution is examined in terms of their Absolute Bias (AB) and Root Mean Squared Error (RMSE) based on 1000 replications. The numerical results of the simulation study indicated that the AB and RMSE of the ML estimates of the parameters for Gompertz distribution decrease with increases in the sample sizes. The real data analysis for Gompertz distribution in the presence of outliers is obtained, where analysis of the waiting times (in minutes) before service of 100 bank customers, confirmed the results of the simulation.