The parameters, i.e. the Period and the Quality factor, of the Earth’s free core nutation (FCN) are closely related to the dissipative coupling between the core and the mantle. Based on the FCN parameters obtained from the actual observations and theoretical simulation, significantly constrained in this study were several key parameters near the core-mantle boundary (CMB), related to the core and mantle coupling, including viscosity at the top of liquid core, conductivity at the bottom of the mantle, and dynamic ellipticity of the CMB. In order to choose high quality observations from global stations of the superconducting gravimeters (SG) on the Global Geodynamics Project (GGP) network, we adopted two criteria, the standard deviations of harmonic analysis on tidal observations and the quality of the FCN parameters calculated with the observations from single station. After the mean ocean tidal effects of the recent ocean tidal models were removed, the FCN parameters were retrieved by stacking the tidal gravity observations from the GGP network. The results were in a good agreement with those in the recent research by using the SG and/or the VLBI observations. Combined with an FCN theoretical model deduced by angular momentum method, the viscous and electromagnetic coupling parameters near the CMB were evaluated. Numerical results indicated that the viscosity at the top of the liquid core was in the range from 6.6×102 to 2.6×103 Pa·s, which was in good agreement with those obtained from the Earth’s nutation, the FCN and variations in the length of day (LOD). The conductivity at the bottom of the mantle should be as large as 2.6×106-1.0×107 S m-1 to match the FCN quality factors from the actual observations. The dissipative coupling had a little influence of 1-2 sidereal days for the FCN period. The parameters, ie the Period and the Quality factor, of the Earth’s free core nut (FCN) are closely related to the dissipative coupling between the core and the mantle. Based on the FCN parameters obtained from the actual observations and theoretical simulation, significantly constrained in this study were several key parameters near the core-mantle boundary (CMB), related to the core and mantle coupling, including viscosity at the top of liquid core, conductivity at the bottom of the mantle, and dynamic ellipticity of the CMB. In order to choose high quality observations from global stations of the superconducting gravimeters (SG) on the Global Geodynamics Project (GGP) network, we adopted two criteria, the standard deviations of harmonic analysis on tidal observations and the quality of the FCN parameters calculated with the observations from single station. After the mean ocean tidal effects of the recent ocean tidal models were removed, the FCN parameters were retrieved by stacking the tidal gravity observations from the GGP network. The results were in a good agreement with those in the recent research by using the SG and / or the VLBI observations. Combined with an FCN theoretical model deduced by angular momentum method, the viscous and electromagnetic Coupling parameters near the CMB were evaluated. Numerical results indicated that the viscosity at the top of the liquid core was in the range from 6.6 × 102 to 2.6 × 103 Pa · s, which was in good agreement with those obtained from the Earth’s nutation, the FCN and variations in the length of day (LOD). The conductivity at the bottom of the mantle should be as large as 2.6 × 106-1.0 × 107 S m-1 to match the FCN quality factors from the actual observations. The dissipative coupling had a little influence of 1-2 sidereal days for the FCN period.