  We study the adiabatic density perturbation in the {\it oscillating
inflation}, proposed by Damour and Mukhanov. The recent study of the
cosmological perturbation during reheating shows that the adiabatic fluctuation
behaves like as the perfect fluid and no significant amplification occurs on
super-horizon scales. In the oscillating inflation, however, the accelerated
expansion takes place during the oscillating stage and there might be a
possibility that the parametric amplification on small scales affects the
adiabatic long-wavelength perturbation. We analytically show that the density
perturbation neglecting the metric perturbation can be amplified by the
parametric resonance and the instability band becomes very broad during the
oscillating inflation. We examined this issue by solving the evolution equation
for perturbation numerically. We found that the parametric resonance is
strongly suppressed for the long wave modes comparable to the Hubble horizon.
The result indicates that the metric perturbation plays a crucial role for the
evolution of scalar field perturbation. Therefore, in the single field case,
there would be no significant imprint of the oscillating inflation on the
primordial spectrum of the adiabatic perturbation. However, it could be
expected that the oscillating inflation in the multi-field system gives the
enormous amplification on large scales, which may lead to the production of the
primordial black holes.
