In this research, we propose a dynamic neural network (DNN) with the characteristics of stiffness, viscosity, and inertia and a training algorithm based on the back-propagation (BP) method to include a momentum term. In a previous research, we proposed a training algorithm for the DNN based on the BP method or GA-based training method. However, in the previous method it was necessary to determine the values of the DNN parameters by trial and error. So, the modified BP method and GA-based training method were designed to train not only the connecting weights but also the property parameters of the DNN. We develop the BP method to include a momentum term in order to increase the convergence of the training effect. Simulation results show that the DNN with characteristics of stiffness, viscosity, and inertia trained by the modified BP method to include the momentum term obtains good training performances for time series signals generated from periodic function. In this paper, we compare the DNN with a conventional training method in order to verify the effectiveness of the DNN.