We theoretically study a non-magnetic impurity effect on the vortex bound states of a multi-quantum vortex. The zero-energy peak of the local density of states is investigated for vortex cores with the winding numbers 2 and 4 within the framework of
the quasiclassical theory of superconductivity. We find that the zero-energy peaks, which appear away from the vortex center in the clean limit, move towards the vortex center with increasing the impurity scattering rate, resolving a contradiction between an experimental result and previous theoretical predictions.
