Recently, intrusion detection systems (IDS) have been introduced to effectively secure networks. Using neural networks and machine learning in detecting and classifying intrusions are powerful alternative solutions. In this research paper, both of Gradient descent with momentum (GDM)-based back-propagation (BP) and Gradient descent with momentum and adaptive gain (GDM/AG)-based BP algorithms are utilized for training neural networks to operate like IDS. To investigate the efficiency of the two proposed learning schemes, a neural network based IDS is built using the proposed learning algorithms. The efficiency of both algorithms is inspected in terms of convergence speed to achieve system learning, and elapsed learning time using various settings of neural network parameters. The result demonstrated that the GDM/AG-based BP learning algorithm outperforms the GDM-based BP learning algorithm.