  In this paper, we show that the inverse anisotropic mean curvature flow in
$\mathbb{R}^{n+1}$, initiating from a star-shaped, strictly $F$-mean convex
hypersurface, exists for all time and after rescaling the flow converges
exponentially fast to a rescaled Wulff shape in the $C^\infty$ topology. As an
application, we prove a Minkowski type inequality for star-shaped, $F$-mean
convex hypersurfaces.
