This paper presents a design method of the Interpolation-based adaptive LQ controller that is accomplished by getting the final controller interpolated with each gain of sub-LQ controllers. The Lagrange interpolation method is used in the scheme. The proposed controller is useful to control nonlinear systems which are especially changed the system parameters. The design method is illustrated by an application to the stabilization and tracking problems of an inverted pole system on a cart. Several cases of simulations are carried out in order to validate the control effectiveness and robustness. The simulation results are compared with those of LQ controller and prove the better control performance than LQ controller.