This paper shows to stabilize a balancing robot. We derive the dynamics of a balancing robot and design its controller using LQR method. For stabilizing balancing robot, we introduce a method to detect an angle using inertial sensors. In this study, we use a complementary filter to fuse signals by frequency response of gyroscope and accelerometer in order to measure the inclined angle of balancing robot. The filter coefficients are obtained by least square to minimize error in angle-detecting filter design. And then, after we derive a dynamics of balancing robot using Lagrange method, we linearize that dynamics for using LQR method.