The doublet anionic states of TCNQ-F4 (2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane) have been studied at the Hartree-Fock and the Moller-Plesset (MP) perturbation theory levels (up to fourth order) with aug(sp)-pVDZ basis sets. Our results indicate that TCNQ-F4 forms a stable anion of 132, symmetry whose vertical electron attachment energy is 2.893 eV (at the MP4 level). In addition, we found two valence excited electronic states (2(2)B(3u) and 1(2)A(g)) of the anion that are stable vertically with respect to the neutral parent. The electronic stability of the third excited state (a core-excited 1(2)B(3u) state) needs to be further investigated. We conclude that the neutral TCNQ-F4 at its equilibrium D-2h geometry may attach an excess electron to form any of,these four states (i.e., 1(2)B(2g), 1(2)B(3u), 2(2)B(3u) and 1(2)A(g)) and the corresponding MP4 vertical attachment energies (VAE) are 2.893, 0.822, 0.244, and 0.072 eV, respectively. However, due to second-order Jahn-Teller distortion, only the ground anionic state (1(2)B(2g)) possesses a minimum at D2h symmetry. For the two valence excited states (2(2)B(3u) and 1(2)A(g)), negative curvatures cause out-of-plane deformations that lead to (i) an increase of the energy of the latter (1(2)A(g)) state and (ii) achieving a minimum-energy structure of C-2 symmetry for the former where this state becomes a doublet A state and its vertical electronic stability increases to 2.721 eV.