We report on the direct generation of passively mode-locked vortex lasers in the visible spectral region, for the first time to the best of our knowledge, using a Pr:LiYF4 (Pr:YLF) crystal as the gain medium. A stable mode-locked TEM00 mode has been achieved with a maximum average output power of 75 mW using a graphene saturable absorber mirror. The mode-locked pulse width is measured to be as short as about 73.4 ps at a repetition rate of about 140 MHz, and the laser wavelength is at about 721 nm with spectral width of about 0.5 nm. By slightly misaligning the laser resonator, a first-order Laguerre-Gaussian mode (LG0,1) has also been obtained with output power reduced to about 22 mW. The achieved LG0,1 mode has been verified via a home made improved Fizeau interferometer. This work provides a simple and universal method for direct generation of an ultrafast vortex laser, which can be readily extended to other spectral regions by using different laser gain mediums.