Based on the 21 series of the high precision tidal gravity observations recorded using superconducting gravimeters (SG) at 14 stations distributed globally (in totally about 86 years), the translational oscillations of the Earth's solid inner core (ESIC) is detected in this paper. All observations are divided into two groups with G-Ⅰ group (8 relatively longer observational series) and G-Ⅱ group (13 relatively shorter observational series). The detailed corrections to minute original observations for each station are carried out, the error data due to the earthquakes, power supply impulses and some perturbations as change in atmospheric pressure and so on are carefully deleted for the first step, the gravity residuals are obtained after removing further synthetic tidal gravity signals. The Fast Fourier Transform analysis is carried out for each residual series, the estimations of the product spectral densities in the sub-tidal band are obtained by using a multi-station staking technique. The 8 common peaks are found after further removing the remaining frequency dependent pressure signals. The eigenperiods, quality factors and resonant strengths for these peaks are simulated. The numerical results show that the discrepancies of the eigenperiods for 3 of 8 peaks, compared to those of theoretical computation given by Smith, are only 0.4%, -0.4% and 1.0%. This coincidence signifies that the dynamical phenomenon of the Earth's solid inner core can be detected by using high precision ground gravity observations. The reliability of the numerical computation is also checked, the spectral peak splitting phenomenon induced by Earth's rotation and ellipticity is preliminary discussed in this paper.