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Two-photon absorption(TPA)spectra of fluorescent proteins show different characters with one-photon absorption(OPA)spectra in the region of short wavelength.The TPA spectra are much stronger than OPA spectra corresponding to the electron transitions from the ground states to highly-lying excited states.Here we mainly put focus on two kinds of chromophores.One is the chromophore of enhanced cyan fluorescent protein which is neutral.Another is the chromophore of red fluorescent protein which is anionic.We utilize the density functional theory(DFT)and the time-dependent DFT to obtain the electronic-structure parameters which enter the TPA expressions.Then their TPA spectra including Franck-Condon and Herzberg-Teller vibronic coupling effects are calculated.The polarizable continuum model is applied with solvent water in order to get better comparison with the experimental results.It is found that the neutral and anionic chromophores possess different TPA properties.