We propose a simple algorithm for obtaining MTL(maximum trimmed likelihood) estimates. The algorithm finds the subset to use to obtain the global maximum in the series of eliminating process which depends on the likelihood of cells in a contingency table. To evaluate the performance of the algorithm for MTL estimators, we conducted simulation studies. The results showed that the algorithm is very competitive in terms of computational burdens required to get the same or the similar results in comparison with the complete enumeration.