An efficient training and pruning method based on the HY filtering algorithm is proposed for feedforward neural networks (FNN). A FNN's weight importance measure linking up prediction error sensitivity obtained from the HY filtering training, and then a weight salience based pruning algorithm is derived. Moreover, based on the monotonicity property of the HY filtering Riccati equation and the initial value of the error covariance matrix, performance of the HY filtering training algorithm will also be investigated. The simulation results show that our approach is an effective training and pruning method for neural networks.