This paper proposes a rigorous nonlinear measurement method of polarization aberrations for the large numerical aperture (NA=0.55) variable-magnification extreme ultraviolet lithography (EUVL) projection objective. First, on the basis of the rigorous variable-magnification extreme ultraviolet (EUV) vector imaging model, the nonlinear overdetermined equations are established with the nonlinear relationships between polarization aberrations and spatial image spectra. Then, a synchronous rotation measurement method is proposed, which constructs and trains a deep neural network algorithm to solve the rigorous nonlinear overdetermined equations and thus achieves the Jones pupil measurement of polarization aberrations for the EUV projection objective with high precision and efficiency. The simulation results show that this method can realize the measurement precision of 10^-4λ (λ denotes the wavelength), which will support the online quality monitoring of EUVL at 3-7 nm technical nodes.