Ytterbium (Yb) doped rare-earth garnet Y3Ga5O12 (YGG) single crystal was grown by the optical floating zone method for the first time, to our knowledge. Its structure and cell parameter were determined by X-ray powder diffraction. The thermal properties of Yb:YGG, including specific heat, thermal expansion coefficient, thermal diffusion coefficient, and thermal conductivity, were investigated. The optical properties of the crystal were also studied and the effective gain cross sections were calculated. With the crystal cut along the 〈111〉 direction, laser performance was also demonstrated by using a laser diode as the pump source. All the results show that Yb:YGG can be an excellent laser medium for applications to tunable and ultrafast pulsed lasers.