  We examine the axion emission from supernovae with a complete set of relevant
axion couplings including the axion-pion-nucleon contact interaction which was
ignored in the previous studies. Two processes are affected by the
axion-pion-nucleon contact interaction, $\pi^-+p \rightarrow n + a$ and
$n+p\rightarrow n+p+a$, and these processes can be the dominant source of
axions for some region in the axion parameter space or in astrophysical
conditions encountered inside supernovae. We find that the contact interaction
can enhance the axion emissivity of $\pi^-+p \rightarrow n + a$ by a factor of
$2-4$, while the effect on $n+p\rightarrow n+p+a$ is not significant. We also
discuss the relative importance of other pion-induced processes such as
$\pi^0+n\rightarrow n+a$ and $\pi^-+\pi^0\rightarrow \pi^-+a$.
