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This paper describes a SOI MEMS oscillating accelerometer with a fully differential CMOS continuous-time read-out circuit. A new ultra-low-noise continuous-time bandpass transimpedance amplifier (TIA) is proposed and serves as the front-end of the read-out circuit. The new TIA topology greatly relaxes the tradeoffs among gain, bandwidth and noise, and achieves a state-of-the-art input referred current noise density of 6.6 fA/ Hz, which helps improve the bias-instability and noise floor of the MEMS oscillating accelerometer. The TIA provides a transimpedance gain of 45 MΩ in the bandwidth from 0.5 Hz to 350 kHz and consumes only 583 µW. To reduce the amplitude-stiffness effect induced frequency variation, the accelerometer employs a displacement control strategy that stabilizes the oscillation amplitude of the MEMS oscillator and a chopper stabilization technique to minimize the flicker noise in the amplitude control block. The accelerometer yields bias-instability of 0.6 µg (Allan Variance) or bias stability of 6.3 µg (1σ in one hour) and 2 µg/ Hz noise floor with 140 Hz/g scale factor and ±20 g full scale. The overall power consumption of the accelerometer is 3.5 mW under a 1.5 V supply.