The Dirichlet distribution is a generalization of the Beta distribution. This research deals with the estimation of scale parameter for Dirichlet distribution with known shapes. We examined three methods to estimate the parameters of Dirichlet distribution which are Maximum Likelihood Estimator, Method of Moment Estimator and Quasi-Likelihood Estimator. The performance of these methods were compared at different sample sizes using Bias, Mean Square Error, Mean Absolute Error and Variance criteria, an extensive simulation study was carried out on the basis of the selected criterion using statistical software packages as well as the application of the criterion to real life data, all these were done to obtain the most efficient method. The simulation study and analysis revealed that Quasi- Likelihood Estimator perform better in terms of bias while Method of Moment Estimator is better than the other two methods in terms of variance; the Maximum Likelihood Estimation was the best estimation method in terms of the Mean square Error and Mean Absolute Error; while Quasi- Likelihood Estimation method was the best estimation method with real life data.