Hadronic axions with the decay constant f(a) congruent-to 10(6) GeV may fulfil 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 3 X 10(5)-3 X 10(6) GeV 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=0.4-0.5 which exceeds slightly the current best bound (rho(a)/rho(nu))NS less-than-or-equal-to 0.3.