We report a simple Nd:YAG laser that emits radially polarized beam with helical wavefront. The laser cavity consists of a piece of laser crystal and a plane output coupler, and there is no additional polarization component inside it. The pump light is converted into annular profile through de-focal coupling into a multi-mode fiber. For the continuous-wave(CW) operation, the laser emits radially polarized vortex beam, and it is observed that the helical wavefront of the laser beam is switched from right handedness to left handedness when the output coupler is tilted slightly. For the Q-switched operation under the insertion of a Cr4t:YAG saturable absorber inside the cavity, we obtain radially polarized outputs with left-handedness helical wavefront. By tilting the laser crystal slightly, the laser output switches to azimuthal polarization at pump power larger than 4.5 W and left-handedness helical wavefront of laser beam is preserved. We report a simple Nd: YAG laser that emits radially polarized beam with helical wavefront. The laser cavity consists of a piece of laser crystal and a plane output coupler, and there is no additional polarization component inside it. For the continuous-wave (CW) operation, the laser emits radially polarized vortex beam, and it is observed that the helical wavefront of the laser beam is switched from right handedness to left handedness when the output coupler is tilted slightly. For the Q-switched operation under the insertion of a Cr4t: YAG saturable absorber inside the cavity, we obtained radially polarized outputs with left-handedness helical wavefront. output switches to azimuthal polarization at pump power larger than 4.5 W and left-handedness helical wavefront of laser beam is preserved.