The outlier elements of a data are ones that differs significantly from others. For many reasons, we have to face with outlier elements in data analysis for the different fields. Because an outlier element can cause the serious problems in statistical analyses, studying about it is interested in many researchers. This article proposes the fuzzy clustering algorithm for outlier - interval data based on the robust exponent distance to overcome the drawback of traditional clustering algorithm which to clean the outliers before performing. The outstanding advantage of this algorithm is to find the suitable number of clusters, to cluster for the interval data with outlier elements, and to determine the probability belonging to clusters for the intervals at the same time. The proposed algorithm is described step by step via numerical examples, and can be performed effectively by the Matlab procedure. In addition, it also applied in reality with the air pollution, mushroom, and image data sets. These real applications demonstrate the robustness of the proposed algorithm in comparison with the existing ones.