Abstract: The approach to deal with the colored noise in Space-Wise LS was discussed in this paper. The AR filter was proposed to process the colored noise in the GOCE satellite gravity gradiometry, which was validated by the numerical results. The PCCG approach method and the direct inverse for solving the large normal equation are also verified by the numerical analysis. And the former approach is much faster than the latter one. Combing the radial component Vzz of the simulated gravity gradient tensor with colored noise and SST observation with white noise, the global gravity field model up to degree and order 180 was estimated by the Space-Wise LS method and the SA approach respectively. The accuracies of geoid and gravity anomaly of the global gravity field model estimated from the Space-Wise LS method are 3.01cm and 0.75mGal respectively, which are better than them from the SA approach.