The presence of common mode error (CME) in the coordinate displacement time series of the Global Navigation Satellite System (GNSS) affects geophysical studies using GNSS observations. In order to investigate the effect of CME on the time series in GNSS networks in Shanxi, this paper proposes an improved superposition filtering method by introducing single-day solution accuracy, correlation coefficient, and spherical distance between stations as weights. The filtering effect is evaluated using the GNSS data in Shanxi. By using the improved stacking filtering method, the root mean square (RMS) values for N, E, U are reduced by approximately 27.8%, 29.0%, and 46.0%, respectively. And compared to the traditional stacking filter, our improved method can achieve better results with CME extraction. We investigate the CME spatial-temporal characteristics and its relationship with environmental loading. The results show that the CME between stations decreases as the distance between stations increases. In addition, we analyze the effect of CME on the noise component and velocity estimates. Results show that removing the CME refines the velocity and leads to a significant reduction in the magnitude of noise, indicating that the CME is dominated by the flicker noise in Shanxi Province.