  One simplified black hole model constructed from a semiclassical analysis of
loop quantum gravity (LQG) is called self-dual black hole. This black hole
solution depends on a free dimensionless parameter P known as the polymeric
parameter and also on the $a_{0}$ area related to the minimum area gap of LQG.
In the limit of P and $a_{0}$ going to zero, the usual Schwarzschild-solution
is recovered. Here we investigate the quasinormal modes (QNMs) of massless
scalar perturbations in the self-dual black hole background. We compute the QN
frequencies using the sixth order WKB approximation method and compare them
with numerical solutions of the Regge-Wheeler equation. Our results show that
as the parameter P grows, the real part of the QN frequencies suffers an
initial increase and then starts to decrease while the magnitude of the
imaginary one decreases for fixed area gap $a_{0}$. This particular feature
means that the damping of scalar perturbations in the self-dual black hole
spacetimes are slower, and their oscillations are faster or slower according to
the value of P.
