The generalized tight-binding model is developed to investigate the magneto-optical absorption spectra of ABC-stacked trilayer graphene. The absorption peaks can be classified into nine categories of inter-Landau-level optical excitations, including three intra-group and six inter-group ones. Most of them belong to the twin-peak structures because of the asymmetric Landau level spectrum. The threshold absorption peak alone comes from a certain excitation channel, and its frequency is associated with a specific interlayer atomic interaction. The Landau-level anticrossings cause extra absorption peaks. Moreover, a simple relationship between the absorption frequency and the field strength is absent. The magneto-optical properties of ABC-stacked trilayer graphene are totally different from those of AAA- and ABA-stacked ones, such as the number, intensity and frequency of absorption peaks.