Detecting the Earth's inner core motions relative to the mantle presents a considerable challenge due to their indirect accessibility. Seismological observations initially provided evidence for differential/super-rotation of the inner core, but recently demonstrated a possibly about 70-year periodic oscillation. The contrasting results underscore the ongoing enigma surrounding inner core motion, leaving debates unresolved, including the precise oscillate period. In parallel to seismic observations, satellite geodesy has accumulated decades of global high-precision records, providing a novel avenue to probe inner core motions. Here, we detect an about 6-year oscillation from the gravitational field degree-2 order-2 Stokes coefficients derived from satellite observations, and find it has a unique phase correlation with the about 6-year signal in the Earth's length-of-day variations. This correlation is attributed to an inner core oscillation which is controlled by the gravitational coupling between the inner core and lower mantle (mainly due to the density heterogeneity of the two large low-velocity provinces; LLVPs). That is, we independently corroborate the inner core periodic oscillation, albeit with a significantly shorter period than previously suggested. Our findings demonstrate the dense layer of the LLVPs (mean density anomalies of about +0.9 percent at the bottom), consistent with inversions from tidal tomography and Stoneley modes. Furthermore, our research reveals equatorial topographic undulations of about 187 m at the inner core boundary.