Influences of variable-angle polarization-rotated optical feedback on polarization properties of vertical-cavity surface-emitting lasers (VCSELs) are investigated numerically. For the so-called case A (x polarization) feedback, only the x mode is selected to pass through the feedback loop. As the polarization angle is varied from $0°$ to $90°$ , the dominant polarization mode switching can be observed even for fixed feedback strength and bias current. For the so-called case B ( $xy$ polarization) feedback, the total outputs of the VCSEL pass through the feedback loop. The polarization property is much different from case A. The dominant polarization mode switching occurs not in the entire range of polarization angles, however, but in the so-called critical angle, from where the intensities of both polarization modes become comparable to each other and keep around constant values, and can be observed. In addition, the complementary properties of intensities between the two polarization modes for both cases are evaluated quantitatively in terms of the defined normalized intensity.