We investigate conversion of a linearly-polarized Gaussian beam to a radially- or an azimuthally-polarized doughnut (0,1) ∗ Laguerre–Gaussian (LG) beams, performed with a spatially-variable retardation (SVR) plate. The SVR plate is composed of eight sectors of a λ/2 retardation plate, each one with different orientation of the to crystal’s slow axis. The analysis reveal that nearly-pure radially- or azimuthally-polarized LG(01) ∗ beam with M 2 =2.2 can be obtained, while the transformation efficiency is 89.6%. In the experiments, performed with Nd:YAG laser, we transformed a Gaussian beam with M 2 =1.3 to a radially- and azimuthally-polarized (0,1) ∗ Laguerre–Gaussian beams with M 2 =2.5. We carefully characterized the polarization state of the obtained radially- and azimuthally-polarized beams, measuring Stokes parameters. The polarization purity of the obtained beams, calculated from the measured data, was as high as 96%.