A trajectory tracking control system design of an autonomous two-wheeled robot (TWR) is presented. The control system objective is to steer the TWR move on a desired trajectory in planar space. The TWR has two kinds of movement: moving forward/backward and turning to the right/left, where the movements are represented by a non-linear kinematics equation. Simplifying the trajectory tracking control system design, the non-linear kinematics equation is approximated by a linear kinematics equation. Linear quadratics regulator (LQR) method is applied to design the trajectory tracking control system. The designed control system is evaluated through computer simulation. Simulation results show that the designed control system is able to make the TWR track a desired trajectory that located 1.4 meter away from the TWR initial position within 3 seconds.