Based on the spin-flip model, the output laser circular polarization switching (PS) and polarization bistability (PB) characteristics of 1300 nm spin vertical-cavity surface-emitting lasers (Spin-VCSEL) under optical pumping are investigated numerically. The results show that, for a certain polarization ellipticity PP of the pump light, the pump power Pout can control the polarization ellipticity of the output light at a certain extent, and its absolute value increases with the increase of pump power. For a certain normalized pump power η, the PS can occur between the left circularly polarized light and the right circularly polarized light of the spin-VCSEL and the PB phenomenon can be observed when PP is scanned forward (gradually increasing) or backward (gradually decreasing). For the small η, the bistability loop width increases to a maximum, and then decreases to 0 with the increasing η. For a large η, the bistability loop width shows a decreasing trend with the increasing η on the whole. Moreover, the internal parameters such as linewidth enhancement factor α of the laser and birefringence coefficient γp of the source medium have a great influence on the PS and PB characteristics induced through the changing of PP. In addition, the distribution of the bistability loop width is also given in the parameter space of some key internal parameters of the laser and η.