Fullerene molecule C60 was studied optimize structure, harmonic vibration frequencies, infrared active vibration modes and some physical values in the gaseous state theoretically by using Density function Theory (DFT), from view animations of the mode displacement patterns, the infrared active vibration modes can be classified theoretically to; Twisting vibration for (=C-C=C-) group at 510.0 cm-1, Wagging vibration for (=C-C=C-) group at 579.8 cm-1, Stretching vibration for (C-C) bond in 1165.6 cm-1 and Stretching vibration for (C=C) bond at 1464.7 cm-1. These results were compared with other calculation data and experimental measurements. Two from these modes are in good agreement with experimental measurement while the two are nearly approach.