The present study deals with one of the most important methods of the robust mixture regression estimators,least trimmed sum of absolute deviations LTA method. It is known that mixture regression models are used to investigate the relationship between variables that come from unknown latent groups and to model heterogenous datasets. In general, the error terms are assumed to be normal in the mixture regression model. However, the estimators under normality assumption are sensitive to the outliers. Therefore, we introduce a robust mixture regression procedure based on the LTA-estimation method to combat with the outliers in the data. In this paper, we handle LTA method by using three mixture regression models; Laplace, and normal distributions. We give a simulation study to illustrate the performance of the proposed estimators over the counterparts in terms of dealing with outliers.