-The purpose is to study the circuit design based on capacitive micromechanical gyroscope. In order to detect a very weak angular rate signal, the signal needs to be properly amplified and demodulated. To this end, an improved continuous-time front-end readout circuit is proposed. The front-end structure is a charge-sensitive amplifier (CSA) with a T-resistor network as a feedback resistor. In order to reduce the noise of the front-end amplifier, the size of the input transistor is optimized accordingly. In addition, in the demodulation process, the comparator demodulation clock signal usually has a certain phase shift. Therefore, this will cause errors in the output signal. For this problem, a simple and effective error correction algorithm is put forward. By the validation of simulation, the results show that the error rate is reduced from 13.7% to 0.3% after the error correction algorithm. Therefore, it can be concluded that the circuit can correctly demodulate the angular rate signal. The algorithm can effectively reduce the error caused by demodulation.