A two-wheeled self-balancing robot system bases on the physical problem of an inverted pendulum. Stabilization of this type of mobile robot requires applying an active control approach. This paper proposes an efficient Linear Quadratic Gaussian (LQG) optimal control for the two-wheeled robot system. The LQG (a combination of a Kalman Filter (KF) and Linear Quadratic Regulator (LQR)) controller is designed to stabilize the robot while reducing the effect of the process and measurement noises on its performance. The LQG controller parameters (elements of state and control weighting matrices of the LQR and KF) are optimally tuned using the Particle Swarm Optimization (PSO) optimization method. The robot stabilization scheme is simulated utilizing MATLAB software to validate the proposed PSO-LQG controller system. The effectiveness of the proposed controller is validated based on the control criteria parameters, which are rise time, settling time, maximum overshoot, and steady-state error. The results prove that the proposed PSO-LQG controller can give very good movement performance in terms of both transient and steady-state responses.