Over the past two decades, Micro-Electro-Mechanical System (MEMS) based accelerometers, benefiting from relatively simple structure, low-power consumption, high sensitivity, and easy integration, have been widely used in many industrial and consumer electronics applications. For the high precision accelerometers, a significant technical challenge is to design a low-noise readout circuit to guarantee the required high resolution of the entire integrated system. There are three main approaches for improvement of the noise and offset of the readout circuit, namely auto-zero (AZ) and correlated double sampling (CDS) for the switched- capacitor (SC) circuit and chopper stabilization (CHS) for the continuous-time circuit. This thesis investigates the merits and drawbacks of all three techniques for reading the capacitance of a low noise MEMS accelerometer developed in our group. After that, we compare the different effects of the three technologies on noise, offset, output range, linearity, dynamic range, and gain. Next, we present the design of the most suitable structure for our sensor to achieve low noise, low offset, and high precision within the working frequency. In this thesis, the design and post-layout simulation of the circuit is proposed, and the fabrication is currently in progress. The readout circuit has reached the noise floor of the sub-μg, which meets the strict requirements of low noise MEMS capacitance-to-voltage converter. A high-performance accelerometer system is regarded as the core of a low-noise, high-resolution geophone. We show that together with the MEMS accelerometer sensor, the readout circuit provides competitive overall system noise and guarantees the required resolution.