  The dispersion relation of the high energy optical \pi-plasmons of simple
hexagonal intrinsic graphite was calculated within the self-consistent-field
approximation. The plasmon frequency \omega_p is determined as functions of the
transferred momentum $q_{\parallel}$ along the hexagonal plane in the Brillouin
zone and its perpendicular component $q_z$. These plasmons are isotropic within
the plane in the long wavelength limit. As the in-plane transferred momentum is
increased, the plasmon frequency strongly depends on its magnitude and
direction (\phi). With increasing angle, the dispersion relation within the
hexagonal plane is gradually changed from quadratic to nearly linear form.
There are many significant differences for the \pi-plasmon dispersion relations
between 2D graphene and 3D AA-stacked graphite. They include $q_\parallel$- and
\phi-dependence and \pi-plasmon bandwidth. This result reveals that interlayer
interaction could enhance anisotropy of in-plane \pi-plasmons. For chosen
$\textbf{q}_\parallel$, we also obtain the plasmon frequency as a function of
$q_z$ and show that there is an upper bound on $q_z$ for plasmons to exist in
graphite. Additionally, the group velocity for plasmon propagation along the
perpendicular direction may be positive or negative depending on the choice of
$\textbf{q}_\parallel$. Consequently, the forward and backward propagation of
\pi-plasmons in AA-stacked graphite in which the energy flow is respectively
parallel or antiparallel to the transferred momentum, can be realized. The
backward flowing resonance is an intrinsic property of AA-stacked graphite,
arising from the energy band structure and the interlayer coupling.
