In this paper, a randomness-enhanced chaotic system model of mutually coupled vertical-cavity surface-emitting lasers (VCSELs) is established by adding anothor injected VCSEL with variable polarizer optical feedback (VPOF). The randomness of chaotic signals is evaluated quantitatively by an information-theory-based quantifier, the permutation entropy (PE). The influences of VPOF-VCSEL rotating polarizer degree, feedback strength, injection strength, mutual coupling strength, path time delay and frequency detuning about injected VCSEL and coupled VCSELs on chaotic signal permutation entropy are numerically studied. It is shown that the chaotic signal permutation entropy of mutually coupled VCSEL system driven by the third VCSEL is much higher than the mutual system with no-driving VCSEL. That is to say, the randomness of coupled system chaotic signal can be enhanced by optical injection. When the rotating polarizer degree is approximately 45 degrees and the injection strength is saturated at a constant level, the system PE can be increased by coupled strength, which is set to be higher than feedback strength. In addition, unequal delay time between both coupled time and feedback time, and higher detuning frequency between driving VCSEL and coupled VCSELs can contribute to randomness-enhanced chaotic signals.