This paper introduces a neural network (NN) -based nonlinear predictor for the LP (Linear Prediction) residual. To evaluate the effectiveness of the NN-based nonlinear predictor for LP-residual, we first compared the average prediction gain of the linear long-term predictor with that of the NN-based nonlinear long-term predictor. Then, the effects on the quantization noise of the nonlinear prediction residuals were investigated for the NN-based nonlinear predictor 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. Experimental results indicate that the prediction gain of the proposed NN predictor was not seriously decreased even when the constrained optimization algorithm was employed.