Fuzzy clustering can be helpful in finding natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in the data. The present paper introduces a new ε-insensitive Fuzzy C-Means (εFCM) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy C-Medians method (FCMED). The performance of the new clustering algorithm is experimentally compared with the Fuzzy C-Means (FCM) method using synthetic data with outliers and heavy-tailed, overlapped groups of the data.