The main advantage of a resonant accelerometer based on electrostatic stiffness over other sensing principles is it can make use of the sensing voltage to adjust the sensitivity. The dynamic model of this accelerometer is built. With the aim to achieve the resonance frequency track, a phase-locked loop(PLL) system is used to track the resonance frequency due to changing of the acceleration, the model for the control system is established and the system behavior are analyzed using an averaging method. The analysis provides a quantitative criterion for selecting the control parameters to achieve system stability, the integral control gain will critical to the system stability and stability time. Simulation results are shown to be in agreement with the all theoretical analysis.