To enlarge the dynamic measurement range of a Micromachined Tunneling Accelerator(MTA) and to improve its performance by reducing the influence of main noise operated in a closed-loop mode，a Linear Quadratic Gaussian (LQG) optimal controller was designed for our MTA to maintain a constant tunneling gap. The linear state space equation for the MTA was deduced, and an Kalman filter and an optimized sate feedback controller were designed. Finally, a simulation system was constructed by combining the Kalman filter and the optimized sate feedback controller in series, and simulation tests were performed. Obtained results show that the bandwidth of the MTA has been increased from 2×103 rad/s to 3×106 rad/s by the optimal control system. Moreover, the fluctuation of the static tunneling current is decreased from 1-2.95 nA to 0.73-1.14 nA from a static test and the distance from the proof mass to the tunneling electrode is effectively regulated to its nominal value of 1 nm under the dynamic square-wave accelerator.