The translational oscillation of the solid inner core is one of the Earth’s fundamental normal modes, which is also called Slichter mode. The normal mode should be split to form a triplet due to the Earth’s rotation and ellipticity. In this study, according to the splitting pattern of Slichter mode, an attempt has been made to detect the possibility of Slichter triplet’s existence by using the product spectra of the long-term continuous gravity measurements from the superconducting gravimeters (SG) at 6 glob- ally-distributed permanent stations in the Global Geodynamics Projects network. The results indicate that the background noise level of the global SG observations is 0.0158 nm s–2 and the magnitude threshold of any global harmonic signals, which may be detected by the global SG, is 0.0152 nm s–2 in the subtidal frequency band from 0.162 to 0.285 cph in which Slichter triplet may occur. it implies that the signatures, related to the triplet, may be identified in the global SG observations, if they exist. It is found that there is a group of global harmonic signatures with the periods of 5.310, 4.995 and 4.344 h emerging significantly from the background noise in the global SG observations. They are in good agreement with the splitting pattern of Slichter mode. It implies that this group of signatures may be related to the inner core translational oscillations. The associated density contrast across the inner core boundary may be deduced as between the values provided in the Earth models of the PREM and 1066 A. The translational oscillation of the solid inner core is one of the Earth’s fundamental normal modes, which is also also called Slichter mode. The normal mode should be split to form a triplet due to the Earth’s rotation and ellipticity. In this study, according to the splitting pattern of Slichter mode, an attempt has been made to detect the possibility of Slichter triplet’s existence by using the product spectra of the long-term continuous gravity measurements from the superconducting gravimeters (SG) at 6 glob- ally-distributed permanent stations in the Global The results indicate that the background noise level of the global SG observations is 0.0158 nm s-2 and the magnitude threshold of any global harmonic signals, which may be detected by the global SG, is 0.0152 nm s-2 in the subtidal frequency band from 0.162 to 0.285 cph in which Slichter triplet may occur. it implies that the signature, related to the triplet, may be identified in the globa l SG observations, if they exist. It is found that there is a group of global harmonic signatures with the periods of 5.310, 4.995 and 4.344 h emerging significantly from the background noise in the global SG observations. They are in good agreement with the splitting pattern of Slichter mode. It implies that this group of signatures may be related to the inner core translational oscillations. The associated density contrast across the inner core boundary may be deduced as between the values ​​provided in the Earth models of the PREM and 1066 A.