A nonlinear multiple regression analysis method based on artificial neural network is developed. The method can resolve nonlinear multiple regression problems effectively, when traditional multiple regression analysis may not capable of doing the job. In this thesis, a new learning algorithm of neural network is developed by using ant colony optimization and back-propagation (BP) learning algorithm. Based on this learning algorithm, the appropriate weight increments of neural network can be computed and decided. Therefore, not only the learning of neural network can be greatly speeded, also the accuracy of neural network''s performance can be effectively improved. For demonstrating the superiority of learning technique, several nonlinear system identification problems were tested. For comparison, same experiments were also performed by network with pure BP learning rule. From the experimental results, the learning technique we developed obviously has better performance as desired.