We study the evolution of convex hypersurfaces X(·,?t) with initial X(’,?0)=θX0 at a rate equal to H-f along its outer normal, where H is the inverse of harmonic mean curvature of X(’,?t), X₀ is a smooth, closed, and uniformly convex hypersurface. We find a θ?>0 and a sufficient condition about the anisotropic function f, such that if θ>θ*,? , then X(’,?t) remains uniformly convex and expands to infinity as t→ +∞ and its scaling, X(’,?t)e-nt, converges to a sphere. In addition, the convergence result is generalized to the fully nonlinear case in which the evolution rate is log H-log f instead of H-f.