Inverted pendulum is a typical underactuation system with multi-variable, nonlinear and strong coupling. Aiming at the control problem of first order inverted pendulum, the mathematical model of inverted pendulum is analyzed and established by Newton-Euler method.The LQR controller was designed based on linear state feedback, and the influence of the weight coefficient of the LQR controller on the control performance was studied. The simulation model was built based on Simscape environment. The experimental results show that the LQR control is stable, the reaction time is fast, and the robustness is strong.