In this paper, we construct the function model of a tunneling accelerometer using MatLab Simulink. With small input signal approximation, the tunneling current and electrostatic actuator nonlinear blocks are analyzed and linearized. From the derived relation between open and close loop transfer functions, we synthesize a simple but effective way to design the control system. By choosing a control system, the accelerometer bandwidth is broadened and the damping is enhanced. The system stability, root locus, step response, gain and phase margins, and pole-zero distribution are all plotted and discussed. With the designed control and feedback systems, a close loop system is stable on both parameter disturbance and frequency response. Compared with the real system at 50 ng Hz-1/2 noise level, we also present tunneling accelerometer characteristics, such as the exponential relationship between tunneling current and displacement change, time history record, dynamics and frequency response.