A diode-pumped self-frequency-doubled Nd,Lu:YA13 (BO3)4 (Nd,Lu:YAB) laser has been operated both continuous wave (cw) and Q-switched. This is a new self-frequency-doubling crystal, which is easier to grow than the related Nd:YAB. Under cw operation, TEM00 mode output powers at the fundamental of 210 mW, or, at the second harmonic wavelength of 531 nm, of up to 24 mW have been obtained, for 880 mW of pump power. When the laser was Q-switched using an acousto-optic modulator, the maximum average power at 531 nm was over 100 mW. The laser operated at pulse repetition rates of up to 70 kHz and delivered pulsewidths in the range of 6-22 ns. These represent the highest visible output power and shortest pulsewidth obtained to date from a diode-pumped Nd:YAB laser.