  In this paper, we consider the evolution of spacelike graphic hypersurfaces
defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center
at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space
$\mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with
the vanishing Neumann boundary condition, and prove that this flow exists for
all the time. Moreover, we can show that, after suitable rescaling, the
evolving spacelike graphic hypersurfaces converge smoothly to a piece of
hyperbolic plane of center at origin and prescribed radius, which actually
corresponds to a constant function defined over the piece of $\mathscr{H}^{n}
(1)$, as time tends to infinity. Clearly, this conclusion is an extension of
our previous work [2].
