In this paper, we discuss training of three-layer neural network classifiers by solving inequalities. Namely, first we represent each class by the center of the training data belonging to the class, and determine the set of hyper-planes that separate each class into a single region. Then according to whether the center is on the positive or negative side of the hyper-plane, we determine the target values of each class for the hidden neurons. Since the convergence condition of the neural network classifier is now represented by the two sets of inequalities, we solve the sets successively by the Ho-Kashyap algorithm. We demonstrate the advantage of our method over the BP using three benchmark data sets.