  We investigate the entanglement spectrum in HOTRG ---tensor renormalization
group (RG) method combined with the higher order singular value
decomposition--- for two-dimensional (2D) classical vertex models. In the
off-critical region, it is explained that the entanglement spectrum associated
with the RG transformation is described by `doubling' of the spectrum of a
corner transfer matrix. We then demonstrate that the doubling actually occurs
for the square-lattice Ising model by HOTRG calculations up to $D = 64$, where
$D$ is the cut-off dimension of tensors. At the critical point, we also find
that a non-trivial $D$ scaling behavior appears in the entanglement entropy. We
mention about the HOTRG for the 1D quantum system as well.
