The continuum-wave laser operation of a new self-frequency-doubled Yb∶Gd0.2Y0.75(BO3)4 (Yb:GdYAB) crystal under high-power diode-end-pumping was reported. To achieve compact all-solid-state laser's operation, a plane-parallel cavity was employed with two mirrors separated by 1 cm, and obtained the fundamental-wave laser with central wavelength at 1044 nm. The maximal output power of 1.38 W was obtained with an absorbed power of 4.22 W, which corresponded to slope efficiency of 54%. A plano-concave cavity was used to obtain efficient self-frequency-doubled (SFD) generation. Self-frequency-doubled green laser with a center wavelength of 522 nm was also obtained, and the threshold absorbed pump power was only 900 mW. The maximal output power was 144 mW when pumped power was 3.9 W. A diode-to-green optical conversion efficiency of 3.7% was achieved. The results indicate that the Yb∶GdYAB crystal is of great potential in applications of both 1 μm fundamental wave and self-frequency-doubled visible light lasers.