This letter addresses a neural network (NN)-based predictor for the LP (Linear Prediction) residual. A new NN predictor takes into consideration not only prediction error but also quantization effects. To increase robustness against the quantization noise of the nonlinear prediction residual, a constrained back propagation learning algorithm, which satisfies a Kuhn-Tucker inequality condition is proposed. Preliminary results indicate that the prediction gain of the proposed NN predictor was not seriously decreased even when the constrained optimization algorithm was employed.