  Recent experiments indicate that AA-stacked bilayer graphenes (BLG) could
exist. Since the energy bands of the AA-stacked BLG are different from both the
monolayer and AB-stacked bilayer graphenes, different integer quantum Hall
effect in the AA-stacked graphene is expected. We have thus calculated the
quantized Hall conductivity $\sigma_{xy}$ and also longitudinal conductivity
$\sigma_{xx}$ of the AA-stacked BLG within the linear response Kubo formalism.
Interestingly, we find that the AA-stacked BLG could exhibit both conventional
insulating behavior (the $\bar{\nu}=0$ plateau) and chirality for
$|\bar{\mu}|<t$, where $\bar{\nu}$ is the filling factor
($\bar{\nu}=\sigma_{xy}h/e^{2}$), $\bar{\mu}$ is the chemical potential, and
$t$ is the interlayer hopping energy, in striking contrast to the monlayer
graphene (MLG) and AB-stacked BLG. We show that in the low-disorder and
high-magnetic-field regime, $\sigma_{xx}\rightarrow0$ as long as the Fermi
level is not close to a Dirac point, where $\Gamma$ denotes the Landau level
broadening induced by disorder. Furthermore, when $\sigma_{xy}$ is plotted as a
function of $\bar{\mu}$, a $\bar{\nu}=0$ plateau appears across $\bar{\mu}=0$
and it would disappear if the magnetic field $B=\pi t^2/Neh\upsilon^2_F$, $N =
1, 2, 3,\cdot\cdot\cdot$. Finally, the disappearance of the zero-Hall
conductivity plateau is always accompanied by the occurence of a $8e^2/h$-step
at $\bar{\mu}=t$.
