We have investigated the ram-pressure stripping of disk galaxies in clusters at various redshifts and in cluster progenitors; the clusters grow up on a hierarchical clustering scenario. We consider a radially infalling galaxy whose initial position and velocity are given by a spherical collapse model of structure formation. Moreover, since observations show that the intracluster medium (ICM) of nearby clusters is non-gravitationally heated, we study the effect of the non-gravitational heating on the ram-pressure stripping. For a given redshift, we find that ram-pressure stripping has more influence on galaxies in more massive clusters. On the other hand, for a given mass, it has more influence on galaxies in the clusters at higher redshifts. In particular, we predict that in rich clusters at z & 1, most of the galaxies are affected by the ram-pressure stripping. While the non-gravitational heating significantly reduces the influence of ram-pressure stripping on galaxies in clusters with mass smaller than 1 5×10 13 M⊙, it does not affect the influence in richer clusters. If the ICM is heated non-gravitationally at z >> 1, rampressure stripping does not occur at z � 1 2 in the progenitors of clusters observed at 0 . z . 0.5, because the heat makes the ICM fraction of the cluster progenitors small. On the other hand, if the ICM is heated non-gravitationally at z � 0 for the first time, the ram-pressure stripping occurs even at z � 3. We compare the results with the observations of galaxies in clusters at various redshifts.