The generation of high-order Laguerre-Gaussian (LG) laser modes at 780 nm from a simple external-cavity diode laser is demonstrated. The beams are derived from computer-generated holograms and a high conversion efficiency of 40% is achieved for LG beams with mode indices from l=1 to l=6. The line width of the external cavity diode laser is below 1 MHz. This system is suitable for studies of trapped and cooled atoms using LG beams.