^{_{We prove the Harnack estimates of curvature flows of hypersurfaces in Rn+1, where the normal velocity is given by a smooth function f depending only on the mean curvature. By use of the estimates, we get some corollaries including the integral Harnack inequality. In particular, we give the conditions, with which the solution to the flow is a translation soliton and an expanding soliton respectively.}}