In an ordinary artificial neural network, individual neurons do not have any special relations with input patterns. That is, an ordinary neural network has only learning capability, but does not have the capability of function localization. However, according to Hebb's cell assembly theory about how the brain worked, it is suggested that it has function localization in the brain, which means that specific groups of neurons are activated corresponding to certain sorts of sensory information the brain receives. On the other hand, it is also reported that the cerebellum and cerebral cortex in the brain are specialized in supervised and unsupervised learning paradigms, respectively. Inspired by both Hebb's cell assembly theory, and the basic learning paradigms in the brain, this paper presents a self-organizing function localization neural network (FLNN). The proposed self-organizing FLNN consists of two parts: the main part and the control part. The main part, corresponding to the cerebellum of brain, is an ordinary 3-layered feedforward neural network, but each hidden neuron contains a signal from the control part, controlling its firing strength. The control part, corresponding to the cerebral cortex of brain, consists of a self-organizing map (SOM) network whose outputs are associated with the hidden neurons of the main part. Trained with an unsupervised learning algorithm, the SOM control part extracts structural features of input space and controls the firing strength of hidden neurons in the main part. And the main part realizes an input-output mapping by using supervised learning. In this way, the self-organizing FLNN realizes the capabilities of both function localization and learning. Numerical simulations show that the self organizing FLNN has superior performance to an ordinary neural network.