Efficient operation at 1040 nm of a diode-pumped Yb:YAl3(BO3)4 laser is reported. A range of cavity configurations has been investigated, as well as output wavelength range. The maximum output power was 654 mW and slope efficiency 71% when pumped with a 1.6 W fibre-coupled diode at 976 nm. Further improvement can be expected with an optimised cavity design. Self-frequency-doubled operation was also demonstrated.