  In this paper, we consider a fully nonlinear curvature flow of a convex
hypersurface in the Euclidean n-space. This flow involves k-th elementary
symmetric function for principal curvature radii and a function of support
function. Under some appropriate assumptions, we prove the long-time existence
and convergence of this flow. As an application, we give the existence of
smooth solutions to the Orlicz-Christoffel-Minkowski problem.
