The molecule of norfloxacin was investigated with the density functional theory (DFT), and the molecular geometry was optimized by utilizing B3LYP method at the levels of 6-311+G(d,p). Based on the optimized geometry, the infrared absorption spectra (IR) and Raman scattering spectra (Raman), the frontier molecular orbital and the net charge distribution were calculated by the means of quantum mechanics. According to the calculation results of the infrared absorption spectra (IR) and Raman scattering spectra (Raman), characteristic vibrational frequencies of norfloxacin molecule were assigned. Based on the calculation results of the highest occupied orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and the net charge distribution, the characteristics of the highest occupied orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and the potential energy surface were discussed. Based on the molecular geometry was optimized by utilizing B3LYP method at the levels of 6-311+G(2d,p), and applying the theory of GIAO, the nuclear magnetic resonance (NMR) was obtained and the spectral data were analyzed and discussed.