The micro electro mechanical system (MEMS) gyroscope has the advantages of small size, high accuracy and broad application prospect. Due to the different thermal stress and thermal resistance of inertial components, the output of the corresponding sensor will produce temperature hysteresis effect, which seriously affects the zero bias stability of gyroscope. In view of the poor adaptability of the traditional gyroscope temperature error compensation method, this paper proposes a temperature hysteresis zero bias compensation model by using the moving average algorithm (MAA) to compensate the zero deviation of MEMS gyroscope in the full temperature range. The experimental results show that when the working temperature of the gyroscope changes in the range of -30 ℃ to +90 ℃ after compensation, the absolute error of the corresponding zero bias decreases from 0.21 (°)/s to 0.02 (°)/s, and the stability of the zero deviation increases by nearly one order of magnitude.