To reduce the influence of the zero-drift problem on the measurement accuracy of an accelerometer and satisfy the measurement accuracy and drift requirements of a low-range micro-electro-mechanical system (MEMS) accelerometer, a high-precision MEMS accelerometer signal processing system based on AD7124 is designed. The hardware uses STM32F303CBT6 as the core controller to drive AD7124, and a high-precision analog-to-digital (A/D) conversion chip is used for data acquisition. In the software, the pulse width modulation (PWM) output square wave is designed as the excitation signal of the accelerometer, and the weighted moving average filter is used to denoise and smooth the signal. An algorithm for zero-drift suppression and tracking is proposed, which solves the problem of excessive zero-drift. After testing, the sensitivity of the accelerometer is 146 mV/g at the ±1 g range, the output stability of the accelerometer after digital filtering is increased by 5.97 times, and the final bias stability is improved from 45.850 mg/h to 0.055 mg/h.