Based on a linear model, a novel method to compensate the polarization aberration of lithographic projection lens is proposed. By using the Hopkins vector theory of partially coherent imaging, the analytical expressions of the aerial image, as well as the image placement error (IPE) and the best focus shift (BFS) induced by the polarization aberrations are derived for the alternating phase-shift mask (Alt-PSM) grating pattern. Based on these analytical expressions, a linear relation model is established between the polarization aberration and the image quality (IPE, BFS). By calculating the polarization aberration linear sensitivities and adjusting the scalar aberrations based on the linear model, the adverse influences of the polarization aberrations on image guality can be minimized, i.e., realizing polarization aberration compensation. The compensation accuracies are dependent on the scalar aberration adjustment accuracy of the projection lens and the sensitivity of the grating pattern to the scalar aberration. The simulation results show that the IPE and the BFS difference of the gratings with different pitches can be effectively reduced, and the image quality can be improved by the polarization aberration compensation method.