We study spin eigenexcitation of a skyrmion in a collinear uniaxial antiferromagnet by means of analytical and numerical methods. We found a discrete spectrum of modes which are localized on the skyrmion. Based on a qualitatively different dependence of the mode eigenfrequencies on the skyrmion radius R0, we divided all localized modes into two branches. Modes of the low-frequency branch are analogous to the localized magnon modes of a ferromagnetic skyrmion, their frequencies scale as R0-2 for the large radius skyrmions, while the modes of the high-frequency branch have no direct ferromagnetic counterpart and do not demonstrate the significant radius dependence and are compactly situated at the magnon continuum. All the modes, except the radially symmetrical one, are doubly degenerated with respect to the sense of rotation around the skyrmion center: clockwise or counterclockwise. An out-of-plane magnetic field removes the degeneracy (for all modes except translational), resulting in a frequency splitting, which for the small fields is linear in field. The possibility of excitation of the modes by means of the external ac magnetic fields is discussed. To explain our numerical results for the low-frequency modes, we introduce a string model for an antiferromagnetic domain wall representing boundary of the large radius skyrmion.