The generation of 343 nm femtosecond laser with high beam quality by the third harmonic generation of an all solid state femtosecond laser was reported. The fundamental harmonic is a commercial Yb:KGW mode-locked laser with a pulse duration of 105 fs, a repetition rate of 76 MHz and a central wavelength of 1 030 nm. Firstly, the second harmonic radiation is achieved with 60% optical-to-optical (1 030 to 515 nm) conversion efficiency. Then, the third harmonic generation based on type Ⅱ and typeⅠ phase-matching BBO crystals are studied respectively. With the type Ⅱ phase-matching BBO, the maximum output power of 0.71 W is achieved under the fundamental power of 5 W, which corresponding to the optical-to-optical conversion efficiency of ~14%. The ultraviolet output power of 1.01 W is obtained corresponding to an optical-to-optical (1 030 to 343 nm) conversion efficiency of 20.2% with type Ⅰ phase-matching BBO. The beam quality of the high power ultraviolet laser at 343 nm is better than 1.3.