Drive current (Isat) of ultrathin germanium-on-insulator (GOI) n-channel metal–oxide–semiconductor field-effect transistors (n-MOSFETs) under full ballistic transport is theoretically investigated for (100)-, (110)-, and (111)-oriented Ge surfaces. The physical origin of the current drive enhancement associated with thinning GOI films for each surface orientation is clarified from the viewpoints of injection velocity (vinj) and inversion-layer capacitance (Cinv). It is found that vinj on (111) is significantly enhanced with decreasing the GOI thickness (TGOI), while no enhancement is observed for (100). This increase in vinj on (111) originates in the increase in the electron occupancy of the lowest subband due to the size effect of ultrathin GOI films. On the other hand, Cinv on (111) slightly decreases with a decrease in TGOI, because of the stronger influence of Cinv due to the density-of-states. In contrast, Cinv on (100) significantly increases with a decrease in TGOI, because of the increase in Cinv due to the inversion-layer thickness, determined by the GOI physical thickness. The (110) GOI surface is found to have intermediate characters between (100) and (111). When Isat is compared under a given gate voltage, the optimum surface orientation is dependent on TGOI and gate oxide thickness (Tox), because of the trade-off relationship in the effective mass between vinj and Cinv. In bulk Ge and GOI with TGOI thicker than around 5 nm, (111) and (110) surfaces can provide the identical and maximum Isat independent of Tox, which is attributed to the higher vinj. In GOI with TGOI thinner than around 5 nm, Isat is higher in the order of (111), (110), and (100) for Tox thicker than around 1 nm, while in the order of (110), (100), and (111) in TGOI thinner than around 1 nm, because of the lowest Cinv on (111). Here, the transition Tox is dependent on TGOI. As a consequence, we can conclude that, in a realistic choice of TGOI and Tox, (111) and (110) surfaces can yield higher Isat in GOI n-MOSFETs.