This paper applied the Characteristic Modelling Theory to a cart-inverted pendulum system. Firstly, the characteristic model of the cart-inverted pendulum is deduced, and the ranges of characteristic parameters are estimated. Secondly, a type of Golden Section Adaptive(GSA) controller with logical integral, logical derivative control law and a gradient descent algorithm to identify the parameters is proposed for the characteristic model. Finally, the designed controller is implemented on the cartinverted pendulum system, and the experiments validate the effectiveness of the designed control law. Compared with the PID, LQR, the proposed method is simpler and easier to implement and has a better performance.