Based on quantum theory and ligand field theory, the E×(b1g+b2g) Jahn-Teller system for C2+4 molecules with the D4h symmetry configuration was studied in this paper using the methods of group theory and symmetry analysis. The symmetry of electronic states and phonon states for the system were explored, the coupling between phonons and CG coefficients were discussed, and the vibronic Hamiltonian for the E×(b1g+b2g) Jahn-Teller system was constructed. The ground state of the system and its energy were calculated using unitary shift transformation. It was found that there were four minima on the potential energy surface of the system because of the vibronic coupling. No matter which minimum the system is in, the ground energy level of the system is split into two energy levels after the Jahn-Teller distortion and the electronic degeneracy of the system is completely lifted. The Jahn-Teller distortion direction for the system was studied further using group theory. The results show that the distortion direction of the system should be D4h→D2h, and the symmetry of the ground state for C2+4 molecules is B1uunder the group D2h after the Jahn-Teller distortion.