  Hadronic axions with the decay constant $f_a\simeq 10^{6}$ GeV may fulfill
all astrophysical and laboratory constraints discussed so far. In this paper,
we reexamine the possibility of the hadronic axion window while taking into
account the uncertainties of some parameters describing low energy axion
dynamics. It is found that $f_a$ in the range from $3\times 10^5$ GeV to
$3\times 10^6$ can not be excluded by existing arguments. We then examine the
implication of this hadronic axion window for the big-bang nucleosynthesis (NS)
by evaluating the energy density of thermal axions at the nucleosynthesis
epoch. Our analysis yields $(\rho_a/\rho_{\nu})_{NS}=0.4\sim 0.5$ which exceeds
slightly the current best bound $(\rho_a/\rho_{\nu})_{NS}\leq 0.3$.
