The time-dependent density functional theory (TD-DFT) was used to obtain vibronic absorption spectra of acridine yellow (AY) dye in an aqueous solution that were in good agreement with the experiment. The protonated and neutral forms of the dye have been investigated. The results of calculations using various functionals and basis sets have been analyzed. The best agreement with experiment was given by the X3LYP/6-31G(d,p) theory level. AY molecular orbitals involved in electronic transitions due light absorption in the visible region of the spectrum have been obtained. The dipole moments and atomic charges of the ground and excited states of the AY molecule have been calculated. Maps of the electrostatic potential and electron densities have been drawn. An insignificant photoinduced electron transfer was found in the central ring of the chromophore of the dye molecule. According to our calculations, the vibronic coupling and the Boltzmann distribution play a significant role in the AY absorption spectra.