  The electronic structure of a vortex line trapped by an insulating columnar
defect in a type-II superconductor is analysed within the Bogolubov-de Gennes
theory. For quasiparticle trajectories with small impact parameters defined
with respect to the vortex axis the normal reflection of electrons and holes at
the defect surface results in the formation of an additional subgap spectral
branch. The increase in the impact parameter at this branch is accompanied by
the decrease of the excitation energy. When the impact parameter exceeds the
radius of the defect this branch transforms into the Caroli--de
Gennes--Matricon one. As a result, the minigap in the quasiparticle spectrum
increases with the increase in the defect radius. The scenario of the spectrum
transformation is generalized for the case of arbitrary vorticity.
