In this paper, a novel robust maximum entropy clustering algorithm RMEC, as the improved version of the maximum entropy algorithm MEC [2-4], is presented to overcome MEC's drawbacks: very sensitive to outliers and uneasy to label them. Algorithm RMEC incorporates Vapnik's ε-insensitive loss function and the new concept of weight factors into its objective function and consequently, its new update rules are derived according to the Lagrangian optimization theory. Compared with algorithm MEC, the main contributions of algorithmRMECexit in its much better robustness to outliers and the fact that it can effectively label outliers in the dataset using the obtained weight factors. Our experimental results demonstrate its superior performance in enhancing the robustness and labeling outliers in the dataset.