The cucurbituril[n] (CB[n]) is a class of chemical supramolecular substances. In order to calculate the spectrum ofthe cucurbituril[n] molecules, the density functional theory (DFT) and the time-dependent density functional theory (TD-DFT) are used to optimize the geometrical structure of CB[n](n=5-10) at the level of 6-311g(d) in the gas phase environment. Then, the infrared (IR) spectrum and ultraviolet (UV) spectrum of CB[n] (n=5-10) are calculated respectively. The results show that: (1) The absorption peaks of two vibration modes of ν(β-H) and ν(γ-H) of CB[n](n = 7,8) are degenerated. (2) The absorption frequency of the stretching vibration ν(α=O) is red shifted. (3) The increase of the absorption peak intensity in the vibration mode near the 1200 cm-1 wavenumber is especially noticeable. (4) The ring tension of CB[n](n=5∼10) gradually decreases with n increasing. (5) The UV absorption wavelength of the maximum absorption peak of CB[n](n=5-10) increases from 198.8317nm to 202.2633nm with n from 5 to 10. The methylene CH2 has isolating action in the formation process of the UV spectrum of CB[n] (n=5-10). The distribution of electron and hole is symmetric and locally excitated (LE) for CB[n] (n=5-10).