An average power of 1.95 W picosecond radially polarized laser was obtained with 1 064 nm at 1 kHz, which based on an all-solid-state picosecond laser developed independently. The peak power of the radially polarized beam was up to 1.77×108 W and the beam quality was measured to be M2=2.95 with the pulse width 11 ps, corresponding to the beam purity of 92%. The radially polarized seed beam was obtained by adding the polarization conversion element outside the laser cavity. In addition, the modulation attenuator caused two different polarization lasers to output the same optical power and then enter the subsequent optical system; and a 0.5 mm thick stainless steel was drilled and grouted by using the obtained picosecond radially polarized laser and picosecond linearly polarized laser under the same processing parameters, respectively. The difference on the circularity of the holes and the depth of the grooves were compared with each other when it was processed by the two polarized picosecond lasers. The results show that the picosecond radially polarization laser has better drilling roundness, deeper notch depth and flatter sidewall of the groove compared to the picosecond linear polarization laser processing results. This results provides a reference for the application of picosecond radial polarization laser in the field of material processing.