Yb-doped yttrium aluminium tetraborate YbxY1-xAl3(BO3)4 (Yb:YAB) has been grown by flux method, with large sizes and good optical quality as well as different Yb3+ ion densities of 8-15at% in the lattice structure. This crystal belongs to the trigonal system with point group 32, conforming space group R32. The density of Yb:YAB is 3.844g/cm3 for a content of 8%. The absorption and fluorescence spectra have been measured. The laser of Yb:YAB crystal can be demonstrated when it is pumped by a laser diode (LD) at a wavelength of 977nm. Cw green output (1.1W) has been obtained with a high beam quality and a diode-to-green optical conversion efficiency of 10%, and wavelength tunablity from 513 to 546nm has been demonstrated. To the best of our knowledge, this is the highest green power achieved for self-frequency-doubling crystals so far.