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High precision accelerometer plays an important role in space scientific and technical applications. A quartz-flexure accelerometer operating in low frequency range, having a resolution of better than 1 ng/Hz1/2, has been designed based on advanced capacitive sensing and electrostatic control technologies. A high precision capacitance displacement transducer with a resolution of better than 2 × 10-6 pF/Hz1/2 above 0.1 Hz, is used to measure the motion of the proof mass, and the mechanical stiffness of the spring oscillator is compensated by adjusting the voltage between the proof mass and the electrodes to induce a proper negative electrostatic stiffness, which increases the mechanical sensitivity and also suppresses the position measurement noise down to 3 × 10-10 g/Hz1/2 at 0.1 Hz. A high resolution analog-to-digital converter is used to directly readout the feedback voltage applied on the electrodes in order to suppress the action noise to 4 × 10-10 g/Hz1/2 at 0.1 Hz. A prototype of the quartz-flexure accelerometer has been developed and tested, and the preliminary experimental result shows that its resolution comes to about 8 ng/Hz1/2 at 0.1 Hz, which is mainly limited by its mechanical thermal noise due to low quality factor.