  We study gravitational and electromagnetic perturbation around the squashed
Kaluza-Klein black holes with charge. Since the black hole spacetime focused on
this paper have $SU(2) \times U(1) \simeq U(2)$ symmetry, we can separate the
variables of the equations for perturbations by using Wigner function
$D^{J}_{KM}$ which is the irreducible representation of the symmetry. In this
paper, we mainly treat $J=0$ modes which preserve $SU(2)$ symmetry. We derive
the master equations for the $J=0$ modes and discuss the stability of these
modes. We show that the modes of $J = 0$ and $ K=0,\pm 2$ and the modes of $K =
\pm (J + 2)$ are stable against small perturbations from the positivity of the
effective potential. As for $J = 0, K=\pm 1$ modes, since there are domains
where the effective potential is negative except for maximally charged case, it
is hard to show the stability of these modes in general. To show stability for
$J = 0, K=\pm 1$ modes in general is open issue. However, we can show the
stability for $J = 0, K=\pm 1$ modes in maximally charged case where the
effective potential are positive out side of the horizon.
