Polycyclic aromatic hydrocarbons are present in interstellar medium and trapped in water ice. Among these compounds, pyrene has a controversial theoretical excitation spectrum. We carried out time-dependent density functional theory, including the long-range correction functionals, with the aim to help to understand the inversion of the first two UV bands of lower energies. The pyrene molecule was optimized at TD-DFT functionals with Def2svp basis set. The spectrum of pyrene molecule was calculated using implicit and explicit solvent models. The explicit solvent effect was studied, including a cluster of 51 water molecules. The implicit solvent PCM model was used with water and benzene as solvents. CAM-B3LYP and ωB97XD give correct band positions and the ω parameter was also optimized. NBO and frontier molecular orbitals were used to study the UV band inversion.