  We investigate highly damped quasinormal mode of single-horizon black holes
motivated by its relation to the loop quantum gravity. Using the WKB
approximation, we show that the real part of the frequency approaches the value
$T_{\rm H}\ln 3$ for dilatonic black hole as conjectured by Medved et al. and
Padmanabhan. It is surprising since the area specrtum of the black hole
determined by the Bohr's correspondence principle completely agrees with that
of Schwarzschild black hole for any values of the electromagnetic charge or the
dilaton coupling. We discuss its generality for single-horizon black holes and
the meaning in the loop quantum gravity.
