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Variable-polarization optical feedback (VPOF) induced unpredictability enhancement in a vertical-cavity surface-emitting laser (VCSEL) is investigated numerically based on the spin-flip model. The chaotic unpredictability is evaluated quantitatively via an information-theory-based quantifier, the permutation entropy (PE). The role of polarizer angle on the chaotic unpredictability is focused on. The influences of feedback strengths, feedback delays, and injection currents are also considered. A critical polarizer angle, at which the PE reaches its maximum, is existed for relatively high feedback strength and injection current. The representations on Poincaré sphere are further given to provide physical insight into the unpredictability enhancement. Besides, larger feedback strength leads to lower critical polarizer angle, while larger injection current contributes to higher critical polarizer angle. These results show that, by selecting critical polarizer angles, the unpredictability of chaotic signals of VCSELs with VPOF can be enhanced significantly, which is extremely useful for VCSELs-based chaotic communication systems.