  In this paper a generalized Gauss curvature flow about a convex hypersurface
in the Euclidean $n$-space is studied. This flow is closely related to the
Orlicz-Minkowski problem, which involves Gauss curvature and a function of
support function. Under some appropriate assumptions, we prove the long-time
existence and convergence of this flow. As a byproduct, two existence results
of solutions to the even Orlicz-Minkowski problem are obtained, one of which
improves the known result.
