An optically pumped vertical-external-cavity surface-emitting laser (VECSEL) for direct emission in the 740-790 nm wavelength region is reported. The gain structure is based on 12 AlGaAs quantum wells. We demonstrate wavelength tuning between 747 nm and 788 nm and free-running operation with a maximum power of 4.24 W (pump power limited) for a heat sink temperature of 14°C. This laser system addresses a spectral gap not currently covered by VECSEL technology and represents the most powerful VECSEL reported within the 7XX-nm wavelength region.