We report, to the best of our knowledge, the first visible-wavelength all-fiber passively mode-locked vortex laser by a figure-9 cavity in combination with <inline-formula><tex-math notation="LaTeX">\sim</tex-math></inline-formula>635 nm mode selective coupler, which can deliver picosecond optical vortex pulses with topological charges of OAM<inline-formula><tex-math notation="LaTeX">_{\pm 1}</tex-math></inline-formula>. The mode-locked vortex laser emits stable rectangular pulses with pulse duration tunable range from 85 to 510 ps and a 0.16-nm narrow linewidth at 634.36 nm. The maximum output power of the vortex laser reaches 1.3 mW with a high purity <inline-formula><tex-math notation="LaTeX">\sim 97.2\%</tex-math></inline-formula>. This work demonstrated the generation of picosecond pulsed vortex in visible passively mode-locked fiber laser, showing their potential for applications in particle trapping, optical tweezers, and high-resolution microscopy.