Abstract: According to the OKADA fault dislocation theory, the model for spatio-temporal inversion of fault slips is built based on Kalman filtering using the GNSS displacement time-space series. To acquire more subtle distribution of a fault slip, the fault is divided into many subfaults. The priori information and the Laplacian smoothing constraint is taken into account. According to the high spatial coherence of surface deformation from fault slip,the spatially-uncorrelated noise is separated effectively by a Kalman filtering inversion of the whole GNSS network. Simulation experiments indicate that since the displacement from the fault deformation is equivalent to the noises level, and GNSS point distribution intervals in strike and dip are equivalent to the length and width of the subfault at least, then the spatiotemporal distribution of the fault slip can be obtained accurately. When the distribution density of the observation stations continues to increase, improvements of the inversion effect are not apparent. However, the high distribution density of stations is very helpful to improve the Signal Noise Ratio(SNR) of the inversion.