The green, red, near-infrared and near-infrared-to-visible upconverted luminescence properties of Er3+/Yb3+ codoped Y3Ga5O12 nanocrystalline powders have been studied using laser spectroscopy. A diffuse reflectance and luminescence spectra confirm that Er3+ and Yb3+ ions occupy the Y3+ sites of the single-phase cubic nano-garnet. Very bright green and red luminescence of the Er3+ ions are detected by the naked eyes, even for a laser power as low as 15 mW, when the Yb3+ ions are excited at 970 nm. The red upconverted emission is more intense than that under direct excitation of the Er3+ ions. The power dependence and the dynamics of the near-infrared-to-green and near-infrared-to-red upconverted emissions show the existence of different two-photon energy transfer upconversion processes. The results here presented indicate that Er3+/Yb3+ codoped Y3Ga5O12 can be a good candidate as an optical nanoheater and nanothermometer in biomedicine applications in the first biological window.