We observe a power-dependent anti-crossing of Walker spin-wave modes under a microwave pump when placing a ferrimagnet in a microwave waveguide that does not support any discrete photon mode. We interpret the unexpected anti-crossing as the generation of a pump induced magnon mode that couples strongly to the Walker modes of ferrimagnet. We realize a remarkable functionality of this anti-crossing, i.e., a microwave frequency comb, in terms of the cross-Kerr nonlinearity that mixes the pump and probe frequencies. Such a frequency comb gets rid of the charge noise from carriers, unlike those produced by diode mixers, and thus may be useful for coherent information conversion with ultra-low noise.