We demonstrate a 266 nm ultraviolet (UV) picosecond laser by fourth-harmonic generation of a Nd:YAG laser with a 5.4 mm thick NaSr3Be3B3O9F4 (NSBBF) crystal. A maximum output power exceeding 1 W at 266 nm was obtained (the highest output power being 1.6 W), corresponding to a conversion efficiency of 10.3%. The stability measurements on the NSBBF crystal with a fluctuation of 3.34% at 200 mW within 1 h indicate that it is a promising UV nonlinear optical material for practical applications. In addition, for the first time, to the best of our knowledge, we measured the effective nonlinear coefficient of NSBBF crystal at 266 nm and compared it with that of β-BaB2O4 crystal.