A new optical single-crystal Yb:CNGS (Yb:Ca₃NbGa₃Si₂O₁₄) was grown successfully for self-frequency-doubling with the sizes of 25 mm in diameter and 50 mm in length using the Czochralski methods. We studied the thermal properties of these crystals systematically, including the thermal expansion coefficient, specific heat, thermal diffusion coefficient, and the thermal conductivity. The absorption and fluorescence spectra of Yb:CNGS crystal were measured. The absorption spectra show a broad transmission range from 350 to 3500 nm. The continuous-wave (CW) laser output at 1060 nm was demonstrated with a- and c-cut crystal. The maximum output power was about 1.53 W under a 4.03 W incident power with z-cut crystals. The slope efficiency was as high as 47.8%. An efficient CW self-frequency-doubling (SFD) green laser was performed with a diode-pumped Yb:CNGS laser. The CW green output power was 37.1 mW and the wavelength tunability from 526 to 532 nm with input pump power as been demonstrated.