In this paper, a new control method for decentralized systems is proposed by using the concept of Nash equilibrium points of non co-operative game. It is supposed that the system stated in this article is composed of many subsystems including their own controllers, so each subsystem can be regarded as a player in the game. And, each subsystem and its controller are described by the Universal Learning Networks which have been proposed to provide a universal framework for the class of neural networks. Based on the above assumptions it is theoretically shown that if the criterion function for each subsystem can be defined individually, then the Nash equilibrium points can be calculated by the gradient learning algorithm. Simulation studies on a decentralized tank network control system show that the Nash equilibrium points can be obtained systematically and effectively by the proposed method.