Abstract: A hidden layer growing mode training strategy is discussed for least squares approximation based three layered feedforward neural networks Firstly, according to the hidden layer output behaviors and expectation data distribution features, the N dimensional space constructed by sample data is divided into several subspaces having different significances, and it is revealed that the output vector of the most effective hidden unit should have its projective component on error space, and the component ought to be positioned in a certain energy space of target space Then a hidden layer growing mode training algorithm is proposed based on energy space approaching strategy Finally, the effectiveness of the algorithm is validated by simulation experiment