In this paper a new robust fuzzy clustering neural networks (RFCNN) is presented to resolve the sensitivity of the fuzzy clustering neural network (FCNN) to outliers in real datasets. The new objective function of RFCNN is obtained by introducing Vapnik’s ε-insensitive loss function, and RFCNN’s update rules are derived by using Lagrange optimization theory. Compared with the FCNN algorithm, RFCNN is much more robust to outliers in the datasets. Experimental results demonstrate the effectiveness of RFCNN.