  We study the QCD vacuum structure under the influence of an electromagnetic
field with a nonzero second Lorentz invariant $I_2=\vec{E}\cdot{\vec B}$. We
show that the presence of $I_2$ can induce neutral pion ($\pi^0$) condensation
in the QCD vacuum through the electromagnetic triangle anomaly. Within the
frameworks of chiral perturbation theory at leading small-momenta expansion as
well as the Nambu--Jona-Lasinio model at leading $1/N_c$ expansion, we quantify
the dependence of the $\pi^0$ condensate on $I_2$. The stability of the
$\pi^0$-condensed vacuum against the Schwinger charged pair production due to
electric field is also discussed.
