The positive-negative circularly polarized four-frequency differential laser gyro (PNDLG) is a novel four-frequency differential laser gyro,it has no optical element except the reflecting mirrors in the cavity,its operating modes are elliptical polarization modes. For the study of PNDLG operating characteristics,the vector self-consistency equations of PNDLG are presented with the elliptical polarization eigenvector mode. Based on the Lamb semi-classical self-consistency field theory,the Lamb coefficients of elliptical polarization modes arederived from the motion equations of the density matrix with the third-order perturbation method. The analysis shows that,Lamb coefficients of elliptical polarization modes can be obtained by those of circular polarization modes multiplying the corresponding ratio,the ratio is the square of the proportion of the positive negative circular polarization electric field component to the whole elliptical polarization electric field amplitude. Finally,the vector self-consistency equations of the PNDLG are built up and proved to be effective by the preliminary experiment,which is useful for the theoretical research on the PNDLG.