We report a numerical study on the internal resonant modes of an antiskyrmion structure in thin-film ferromagnetic nanodisks by using micromagnetic simulations. As the samples are excited by an oscillating magnetic field along different directions, we are able to resolve several sets of resonant eigenmodes: gyrotropic mode and azimuthal and radial spin wave modes. At the in-plane field excitation, the gyrotropic mode at the low frequency behaves consistently with Thiele's analytic theory, while a pair of twin azimuthal spin wave modes at higher frequencies demonstrate that their splitting is strongly relevant to the coexistent gyrotropic mode. At the out-of-plane field excitation, several breathing-like radial spin wave modes have been found. In addition, we carry out a brief comparison between these modes and their counterpart modes of an isolated skyrmion structure. We also quantitatively investigate the dependence of the eigenfrequencies of these modes on the different parameter sets of the sample size and internal interactions, which exhibit complex relationships between the internal dynamic modes of an antiskrymion and the geometry and material of the sample.