We demonstrate the direct generation of visible vortex beams at 640 nm and 607 nm by employing an off-axis pumping scheme in a diode end-pumped Pr3+:YLF laser. A detailed numerical analysis, based on the coherent superposition of Hermite-Gaussian modes with different amplitudes and phases, is perfectly consistent with the experimentally observed lasing modes. The maximum vortex output powers have been measured to be 808 mW and 211 mW at a pump power of 3.16 W, for the wavelengths of 640 nm and 607 nm, respectively. We also demonstrate the handedness control of the generated vortex beam. Such a visible vortex laser can potentially be applied in super-resolution fluorescent microscopes and micro-fabrication research.