The random drift of a micro-electromechanical system (MEMS) gyroscope seriously affects its measurement accuracy. To model and compensate its random drift, the time series analysis method has widely been deployed, which, however, requires a large amount of data for pre-processing analysis and is unsuitable for real-time applications. This paper proposes a new random drift compensation method based on the adaptive Kalman filter (AKF) and phase space reconstruction (PSR). AKF is first designed to compensate the random drift of the low-cost MEMS gyroscope. The phase variables are then used as phase vectors via PSR. Experiments show that the proposed AKF-PSR method can effectively compensate the random drift of the gyroscope, and the standard deviation is reduced by half.