I show that the upper bound of the classical QCD axion window can be significantly relaxed with low-scale inflation.
If the Gibbons-Hawking temperature during inflation is lower than the QCD scale and the inflation lasts long enough, the initial QCD axion misalignment angle follows the Bunch-Davies distribution. The distribution is peaked at the strong CP conserving minimum if there is no other light degree of freedom contributing to the strong CP phase. As a result, the axion can be the dark matter even for an axion decay constant much larger than 10^{12} GeV. On the other hand, if there is mixing between the inflaton and the QCD axion, the QCD axion can be set at the hilltop of the potential after the inflation. In this case, the QCD axion dark matter with decay constant around 10^{9-12}GeV can be possible.
