The theoretical investigations on the molecular energy levels, energy gaps, and the singlet-singlet electronic excitation properties (such as absorption spectra, excited energy, oscillator strengths) of the anthracene molecule in different external electric field were carried out by employing density functional theory (DFT) and time-dependent density functional theory (TDDFT) method with 6-311G(d, p) basis set. The stable molecular structure in ground state was optimized by DFT. The calculated results show that the absorption bands of anthracene molecule concentrate in ultraviolet region without external electric field, the absorption peak of which corresponds to the S0→S5 transitions with an excitation wavelength of 234.5 nm. The calculated absorption spectra agree well with the experimental data. Moreover, it is noticeable that the effects of the external electric field on optical properties cannot be neglected. The ultraviolet absorption spectra of anthracene molecule show a red shift into the blue-light region with the increases of electric field intensity. At the same time, the energy gaps between LUMO and HOMO for the anthracene molecule decrease with the increase of external electric field intensity. It can be shown that the anthracene molecule is promising as a useful blue-light emitting material through modulating by an electric field.