We present in this study a new and robust algorithm for feed-forward neural network (NN) fitting. This method is developed for the application in potential energy surface (PES) construction, in which simultaneous energy-gradient fitting is implemented using the well-established Levenberg-Marquardt (LM) algorithm. Three fitting examples are demonstrated, which include the vibrational PES of H2O, reactive PESs of O-3 and ClOOCl. In the three testing cases, our new LM implementation has been shown to work very efficiently. Not only increasing fitting accuracy, it also offers two other advantages: less training iterations are utilized and less data points are required for fitting. (C) 2015 Elsevier B.V. All rights reserved.