The backpropagation (BP) algorithm allows multilayer feedforward neural networks to learn input-output mappings from training samples. Due to the nonlinear modeling power of such networks, the learned mapping may interpolate all the training points. When erroneous training data are employed, the learned mapping can oscillate badly between data points. In this paper we derive a robust BP learning algorithm that is resistant to the noise effects and is capable of rejecting gross errors during the approximation process. The spirit of this algorithm comes from the pioneering work in robust statistics by Huber and Hampel. Our work is different from that of M-estimators in two aspects: 1) the shape of the objective function changes with the iteration time; and 2) the parametric form of the functional approximator is a nonlinear cascade of affine transformations. In contrast to the conventional BP algorithm, three advantages of the robust BP algorithm are: 1) it approximates an underlying mapping rather than interpolating training samples; 2) it is robust against gross errors; and 3) its rate of convergence is improved since the influence of incorrect samples is gracefully suppressed.