This paper presents a new neural network based on fuzzy set and its application to invariant character recognition. The fuzzy neural network consists of five layers. The results of simulation show that the network can recognize characters in the case of distortion, translation, rotation and different sizes of handwritten characters and even with noise(8${sim}$30%)). Translation, distortion, different sizes and noise are achieved by layer L2 and rotation invariant by layer L5. The network can recognize 108 examples of training with 100% recognition rate when they are shifted in eight directions by 1 pixel and 2 pixels. Also, the network can recognize all the distorted characters with 100% recognition rate. The simulations show that the test patterns cover a ${pm}20^{circ}$ range of rotation correctly. The proposed network can also recall correctly all the learned characters with 100% recognition rate. The proposed network is simple and its learning and recall speeds are very fast. This network also works for the segmentation and recognition of handwritten characters.