  We consider the scenario in which the Peccei-Quinn symmetry breaking is
followed by a period of inflation. A particularly interesting case is that the
string-domain wall network produced by the symmetry breaking enters the horizon
after the QCD phase transition. We show that the abundance of axions produced
by such a string-domain wall network is counterintuitively much larger than the
conventional post-inflationary Peccei-Quinn symmetry breaking scenario. As a
result, a scenario with the axion decay constant even as low as the
astrophysical bound of about $10^8$ GeV can explain the observed abundance of
dark matter. The axion mini-halos produced from the string-domain wall network
is much more massive than the conventional scenario. We also briefly discuss
models which can realize this scenario such as a Peccei-Quinn phase transition
during inflation or a second inflation after a Peccei-Quinn phase transition.
