In order to decrease the nonlinearity of a Micromechanical Tunneling Gyroscope(MTG), enlarge its band width and raise the signal-to-noise ratio of the system, the tunneling gap between the tunneling tip and the corresponding tunneling electrode should be controlled in 1 nm, moreover the MTG must operate in the closed-loop mode. Based on the anti-interference and robustness of the Linear Quadratic Gauss(LQG) control theory and time-varying characteristics of Coriolis acceleration, this paper uses the predictive-LQG control strategy formed by a series of time-varying Kalman filter and an optimal LQG controller to design a closed-loop control system for the MTG. First, the overall control scheme was designed according to the operating principle of the MTG. Then, the two series of the predictive-LQG controllers were designed on the basis of the establishment of the extended dynamic equation of the MTG. Finally, the predictive-LQG controller system of the MTG was built up by Simulink, and a numerical simulation was performed. The simulation results prove that the tunneling gap has been controlled in 1 nm and the measured input angular rate could be estimated accurately by the predictive-LQG controller even if the input angular rate is a slowly varying random signal. And the estimation accuracy can reach 10-4rad/s.