  We study the massless scalar wave propagation in the time-dependent
Schwarzschild black hole background. We find that the Kruskal coordinate is an
appropriate framework to investigate the time-dependent spacetime. A
time-dependent scattering potential is derived by considering dynamical black
hole with parameters changing with time. It is shown that in the quasinormal
ringing both the decay time-scale and oscillation are modified in the
time-dependent background.
