We propose a simple method to generate broadband polarization chaos using two mutually coupled free-running vertical-cavity surface-emitting lasers (VCSELs). Specifically, we quantitatively investigate the effect of critical external parameters (bias current, frequency detuning and coupling coefficient) on the polarization chaos bandwidth in the scenarios of parallel injection and orthogonal injection, and reveal the physical mechanism of bandwidth enhancement in two scenarios. Final simulation results show that the bandwidth of chaotic signals obtained from parallel and orthogonal injection can reach 35.15 GHz and 32.96 GHz, respectively.