Magnetic skyrmions in bulk crystals are line-like topologically protected spin textures. They allow for the propagation of magnons along the skyrmion line but are localized inside the skyrmion line. Analogous to the vortex line, these propagating modes are the Kelvin modes of a skyrmion line. In crystals without an inversion center, it is known that the magnon dispersion in the ferromagnetic state is asymmetric in the wavevector. It is natural to expect that the dispersion of the Kelvin modes is also asymmetric with respect to the wavevector. We study the Kelvin modes of a skyrmion line in the ferromagnetic background. In contrast, we find that the lowest Kelvin mode is symmetric in the wavevector in the low energy region despite the inversion symmetry breaking. Other Kelvin modes below the magnon continuum are asymmetric, and most of them have a positive group velocity. Our results suggest that a skyrmion line can function as a one-way waveguide for magnons.Lord Kelvin calculated stable propagating wave modes along a straight vortex tube of uniform vorticity in a classical fluid about 130 years ago. 1 These modes were later called Kelvin modes. The Kelvin modes in quantized vortex lines were subsequently studied 2,3 and observed experimentally 4 in quantum superfluids. The spectrum of the Kelvin modes in the long wavelength limit is ω = 2 k 2 2m ln(1/kξ), where m is the mass of a particle in the superfluid, k is the momentum, and ξ is the healing length.