A neodymium-doped gadolinium scandium gallium garnet (Nd:GSGG) single crystal with dimensions of Φ 5×20mm2 has been grown by means of optical floating zone (OFZ). X-ray powder diffraction (XRPD) result shows that the as-grown Nd:GSGG crystal possesses a cubic structure with space group Ia3d and a cell parameter of a=1.2561nm. Effective elemental segregation coefficients of the Nd:GSGG as-grown crystal were calculated by using X-ray fluorescence (XRF). The thermal properties of the Nd:GSGG crystal were systematically studied by measuring the specific heat, thermal expansion and thermal diffusion coefficient, and the thermal conductivity of this crystal was calculated. The absorption and luminescence spectra of Nd:GSGG were measured at room temperature (RT). By using the Judd–Ofelt (J–O) theory, the theoretical radiative lifetime was calculated and compared with the experimental result. Continuous wave (CW) laser performance was achieved with the Nd:GSGG at the wavelength of 1062nm when it was pumped by a laser diode (LD). A maximum output power of 0.792W at 1062nm was obtained with a slope efficiency of 11.89% under a pump power of 7.36W, and an optical–optical conversion efficiency of 11.72%.