Based on a spin-flip model (SFM) of vertical-cavity surface-emitting lasers (VCSELs), this paper theoretically investigates the characteristics of polarization switching (PS) and polarization bistability (PB) in the VCSEL subject to continuous variable-polarization optical injection. The results show that in the case of reasonable injection parameters, PS and PB effects of the polarization components of the VCSEL can be induced by the polarization angle of the injection light when the angle is continuously scanned along the forward and reverse routes. Meanwhile, the forward and reverse PS points shift with the scan period, leading to a variable width of the PB region. For a given injection intensity, the forward and reverse PS points exhibit opposite changing patterns with the increase in scanning period. Moreover, a shorter scanning period and a larger frequency detuning are both conducive to a wider PB region. When the frequency detuning is fixed, the change in injection light intensity also has a great influence on the PS position and the PB width. A weak injection intensity and a short scanning period are both conducive to expanding the PB width. When injection intensity and frequency detuning are fixed, both the polarization angles corresponding to forward and reverse PS points demonstrate an approximate uptrend with an increasing bias current, whereas the width of the PB region experiences violent fluctuations. Furthermore, a longer scanning period leads to a smaller PB width. Additionally, the spin-flip rate also has an impact on the PS and PB characteristics of the output polarization components of the VCSEL. A lower spin-flip rate is more liable to result in a larger PB width for given injection parameters.