Propagation of polarized light through a scattering medium has been studied with a Monte Carlo code to obtain polarized backscattered images. Studies of these backscattered patterns obtained with polarized illumination can be used as a technique to characterize the medium anisotropy factor g. First we present the different steps of the Monte Carlo simulation that describe polarized light propagation in a turbid medium. Monte Carlo is a good tool to simulate the backscattered polarized light but is time-consuming. Therefore, we consider two ways to decrease the computation time. The first way deals with angle sampling of the light direction. The second takes advantage of backscattered image symmetry to divide the simulation time by a factor of 4. By combining these two techniques we significantly decrease the code computation time.