Abstract: In this paper, a probability limit property is proposed for the weight vectors W of feedforward neural network （FNN） when both the input data and output data contain noise or when only the output data contain noise. By theory analysis of error function for FNN, two conclusions are obtained as follows:① Recently, many researches focus on training the network so that minimization of the least squares error function is possible. Because of this paper’s conclusion having nothing to do with algorithm, and thus, when using noisy inputs and outputs, it is impossible to improve the fitting capability between network and system by only improving algorithm. ② Although in most cases the least squares error function is used, this function is not a good choice when a FNN is trained with noisy input output patterns. In order to improve the fitting capability between network and system, a new error function must be adopted. These results are good enough for future research.