  We examine the theoretical possibility for the heavy QCD axion to induce
slow-roll inflation while solving the strong CP problem through the
Peccei-Quinn mechanism. If the cancellation between contributions from a
small-size instanton and another Peccei-Quinn symmetry breaking occurs with
high accuracy, the potential can be flattened enough near its maximum to
achieve hilltop inflation. This comes at the cost of severe fine-tuning of
their relative size and phase, but it also allows us to relate the high quality
problem of the Peccei-Quinn symmetry to the fine-tuning problem of the hilltop
inflation. There are two classes of such axion hilltop inflation, each giving a
different relation between the axion mass at the minimum and the decay
constant. The first class predicts the relation $m_\phi \sim 10^{-6}f_\phi$,
and the axion can decay via the gluon coupling and reheat the universe. Most of
the predicted parameter region will be covered by various experiments such as
CODEX, DUNE, FASER, LHC, MATHUSLA, and NA62 where the production and decay
proceed through the same coupling that induced reheating. The second class
predicts the relation $m_\phi \sim 10^{-6} f^2_\phi/ M_{\rm pl}$. In this case,
the axion mass is much lighter than in the previous case, and one needs another
mechanism for successful reheating. The viable decay constant is restricted to
be $10^8{\rm GeV} \lesssim f_\phi \lesssim 10^{10}\,$GeV, which will be probed
by future experiments on the electric dipole moment of nucleons. In both cases,
requiring the axion hilltop inflation results in the strong CP phase that is
close to zero.
