  A variant of the Gauss curvature flow for closed and convex hypersurfaces is
considered. We reveal that if the initial hypersurface is pinched enough, then
this property is preserved. Furthermore, based on some structure assumptions on
the speed function of the shrinking flow, we show that the flow converges to a
sphere. This may generalize the result of B. Chow\cite{CW85} to the possible
non-homogeneous curvature flows.
