Abstract: When neural network （NN） is applied to practical engineering, there are more or less some noises or outliers in training data sets. To make NN hold more robust, a novel robust estimation function is proposed to serve as new target function of feedforward neural network （FNN） according to the theorem of robust statistics in the paper. The results of the theoretical analysis and simulation for function approximation problem show superiority of the method, which not only holds basically the merit of the least square estimate （LSE） method but also has robustness against outliers.