  In this article, we investigate a flow of inverse mean curvature type for
capillary hypersurfaces in the half-space. We establish the global existence of
solutions for this flow and demonstrate that it converges smoothly to a
spherical cap as time tends to infinity. As a result, we derive a new
Minkowski-type inequality for star-shaped and mean convex capillary
hypersurfaces for the whole range of contact angle $\theta\in (0,\pi)$.
