Based on the density functional theory DFT/B3LYP at 6-311++g(d, p) level, the ground states of GaN molecule under different external electric fields were optimized. The influence of external electric field ranging from 0 to 0.025 a.u. on the geometrical parameters, dipole moment, total energy, energy gap, Infrared spectrum, Raman spectrum and UV-VIS absorption spectrum intensity were studied. The results showed that the changes of molecular structure were strongly dependent on the applied electric field. As the electric field changed from 0 to 0.025 a.u., the bond length of GaN molecular decreased, while the electric dipole moment was proved to be decreasing and the total molecular energy increased all the time. The energy gap of Eg was found to decrease with the increasing external field. The IR vibration spectrum of GaN molecule showed an observable blue shift and the Raman vibration spectrum appears blue shift phenomenon too. The oscillator strength of UV-VIS absorption spectrum was proved to be repeating the changes of the first decreasing and then increased. The ultraviolet absorption peak was red-shifted with the increase of the field intensity.