Simple periodic one-dimensional (1D) common photonic crystals (PCs) doped with InSb are proposed to research the Faraday rotation (FR) effect by applying a 4×4 transfer matrix method. Analysis indicates that the given 1D PCs can realize a giant FR angle. The influences of the properties of InSb (magnetic induction intensity, temperature, and the length of the InSb layer) and the repeat number of the structure on the FR are investigated due to the tunability of InSb and the features of the structure. Through calculation, it is found that, by adjusting these parameters, we can clearly observe the movement of the extreme values of the FR angle. In addition, the numerical results show that when the magnetic induction intensity and the repeat number of the structure are changed, the FR angle will be significantly altered at the fixed extreme frequency point. Specifically, if the temperature and the thickness of InSb layer are altered, the extreme value of the FR and the frequency point where it happens also will change. We believe these obtained results can provide ideas to design optical isolators and optical switches.