Based on the linear electro-optic effect with quasi-phase matching in periodically poled LiNbO3 crystal, the evolution laws of the output laser polarization with the applied electric field were explored by means of Poincare sphere theory, under different duty ratio of the crystal and temperature. It is found that the evolution of the output laser polarization is very sensitive to the applied electric field E0, the crystal duty ratio D and the crystal temperature T0. With T0 fixed at 273 K, and D fixed at 0.25, 0.5 and 0.75, the output polarization appears periodical evolution with the increase of E0. If D is 0.5, and T0 are 263 K, 293 K and 313 K, evolution of the laser polarization show irregular. Arbitrary polarized light can be performed by reasonable selection of a certain applied electric field, duty ratio and temperature. These results are helpful in optimizing design of the polarization controller based on PPLN crystal.