In this paper, an interval wavelets neural networks is proposed as an alternative to feedforward neural network for approximating arbitrary nonlinear functions. Different from the past ones, the present work has main characteristics as follows: (1) using interval wavelet space as the basic learning space of neural networks, the authors have solved the problem in which basic space does not match the space of learnt signals. (2) As interval wavelets theory is used, the authors have overcome the discontinuity problem caused by enlarging learnt signals in order to adapt basic space of neural network. The number of neurons is decreased, which is greatly notable in high-dimensional situations. (3) The activity functions of neurons are not the same functions.