This paper presents a self-organizing function localization neural network (FLNN) inspired by Hebb's cell assembly theory about how the brain worked. The proposed self-organizing FLNN consists of two parts: main part and control part. The main part 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 consists of a SOM network whose outputs are associated with the hidden neurons of the main part. Trained with an unsupervised learning, SOM control part extracts structural features of input-output spaces and controls the firing strength of hidden neurons in the main part. Such self-organizing FLNN realizes capabilities of function localization and learning. Numerical simulations show that the self-organizing FLNN has superior performance than an ordinary neural network.