Vibronic coupling constants of Jahn-Teller molecules, benzene radical cation and anion, are computed as matrix elements of the electronic part of the vibronic coupling operator using the electronic wave functions calculated by generalized restricted Hartree-Fock and state-averaged complete active space self-consistent-field methods. The calculated vibronic coupling constants for benzene cation agree well with the experimental and theoretical values. Vibronic coupling density analysis, which illustrates the local properties of the coupling, is performed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. This analysis reveals that the couplings of the e2g2 and e2g3 modes in which the large displacements locate on C-C bonds are strong in the cation. On the other hand, they are greatly weakened in the anion because of the decrease of electron density in the region of the C-C bonds, which originates from the antibonding nature of the singly occupied molecular orbital of the anion. However, the difference of the electronic structure has a little influence on the vibronic coupling of the e2g4 mode. These results indicate that the vibronic coupling depends not only on the direction of the nuclear displacement but also on the frontier electron density.