Abstract: Based on the two-level and multi-level models, the AC Stark shift of the 5S1/2 and 5P3/2 states of 87Rb atoms in an Optical Dipole Trap(ODT) formed by a strongly-focused single Gaussian laser beam is analyzed and calculated. For performance of molasses cooling of 87Rb atoms in the Far-off-resonance Trap(FORT) by 852 nm Gaussian laser beam, the AC Stark shift of 5S1/2F=2-5P3/2F'=3 cycling transition for cooling is also calculated, results show that the frequency shift has an important impact on the molasses cooling process. Furthermore, the AC Stark shift of 87Rb 5S1/2|F=2,|mF=2〉 and 5P3/2|F'=3,|mF=3〉 states versus the wavelength of the ODT laser is analyzed, which shows that there is no magic wavelength for 5S1/2-5P3/2 transition of 87Rb atoms in the red-off-resonance condition.