In this paper, the decentralized neural network control of the reference compensation technique is proposed to control a 2-DOF inverted pendulum on an x-y plane. The cart with the 2-DOF inverted pendulum moves on the x-y plane and the 2-DOF inverted pendulum rotates freely on the x-y axis. Since the 2-DOF inverted pendulum is divided into two 1-DOF inverted pendulums, the decentralized neural network control is applied not only to balance the angle of pendulum, but also to control the position tracking of the cart. Especially, a circular trajectory tracking is tested for position tracking control of the cart while maintaining the angle of the pendulum. Experimental results show that position control of the inverted pendulum system is successful.