In this paper,a self-mode-locked Nd:YVO4 picosecond vortex laser is demonstrated, which can operate on the different Laguerre-Gaussian (LG) modes at 1 064 nm. A π/2 mode converter is utilized to realize the picosecond vortex laser with LG mode transformed from the high-order Hermite-Gaussian (HG) mode. For the proposed laser, the mode-locked pulse repetition rate is 1.81 GHz. The average output powers of LG12 mode and LG02 mode are 1.241 W and 1.27 W, respectively, and their slope efficiencies are 23.2% and 24%, respectively.