Geocenter motion, defined as the motion of center of mass (CM) of the Earth relative to the center of figure (CF), reflects the mass redistribution in Earth system, so accurately estimated geocenter motion has a significant contribution for understanding the mass variation of the Earth. In the study, geocenter motions are determined accurately using the combination of GRACE gravity solutions with altimeter observations or ocean models. The estimates derived from the combination of GRACE and ocean models agree well with previous researches. However, since the altimeter measurements refer to International Terrestrial Reference Frame (ITRF), which is different from CF, and data and models also contain errors, estimated geocenter motions from the combination of GRACE and altimeter data show the discrepancies compared to previous studies, especially in phases and trends. The study also analyzes the impacts of leakage effects and the degree one coefficients of Post-Glacial Rebound (PGR) on determining geocenter motions. The result shows that leakage effects have to be considered in computation. When non-zero degree one coefficient of PGR is applied, only about 80% of the change of assumed degree one PGR reflects on the trend of the estimated geocenter motion.