The high-speed polarization state rotation associated with the polarization multiplexing coherent optical communication system link causes channel damage. Further, the feedback delay associated with the dynamic equalization algorithm module of the coherent receiver in the actual system results in insufficient polarization state tracking performance. In this study, a tracking and prediction algorithm for polarization state rotation is proposed based on complementary Stokes vectors to resolve the aforementioned problems. The proposed algorithm initially transforms the measured polarization rotation matrix of the Jones space and its inverse matrix into the Stokes space, obtains a pair of complementary vectors, and tracks and predicts the motion trajectories of the complementary vectors in Stokes space. Finally, the compensation of the polarization state rotation of the link is realized. The simulation results show that the squared error of the predicted Jones matrix can be reduced by 10% compared with that in the original scheme by tracking the complementary vector when the equalization feedback delay is 5 frames. Furthermore, the polarization rotation speed tolerance of the system increases from 1.3 MHz to 1.5 MHz when using the proposed algorithm.