For the first time,we present a quasi-three-level Yb∶YAG laser operating in continuous wave（CW） mode.It is based on the 2F5/2-2F7/2 transition and outputs 1024 nm wavelength.The use of a pump module with 16 light passes through the crystal allows the realization of a folded cavity Yb∶YAG thin-disk laser with 370 mW output power at 1024 nm when the pump power is 32.2 W.Moreover,intra-cavity second-harmonic generation（SHG） has also been achieved with a power of 45 mW at 512 nm by using a LiB3O5（LBO） nonlinear crystal.The power stability in 30 minutes is better than ±4.3%.