An efficient all-solid-state picosecond (ps) ultraviolet (UV) laser at 335 nm was demonstrated based on frequency quadrupling of a mode-locked 1342 nm MOPA system. An output power of 0.95 W was obtained under a fundamental wave power of 16.38 W, corresponding to a conversion efficiency of 5.8% from infrared to UV. The repetition rate and pulse duration were 77 MHz and 20.2 ps, respectively. The beam quality factor M(2) was measured to be 1.56. This is, to the best of our knowledge, the highest output power at 335 nm.