In this paper we investigate the effects of the large extra dimensions on the two processes e+ e → H0 Z0 Z0 and e+e- → H0H0Z0 at linear colliders in both unpolarized and polarized collision modes. We find that the virtual Kaluza-Klein graviton exchange can significantly enhance the cross section from their standard model expectations for these two processes. The results show that the LED effect on the process e+ e- → H0 Z0 Z0 allows the observation limits on the effective scale Ms to be probed up to 9.75 TeVand 10.1 TeV in the unpolarized and +-(λe+ = 1/2, λe- = -1/2) polarized beam collision modes (with Pe+ = 0.6, Pe- = 0.8), respectively. For the process e+ e- → H0 H0 Z0, these limits on Ms can be probed up to 6.06 TeV and 6.38 TeV in the unpolarized and polarized collision modes separately. We find that the λe+ = 1/2, λe- = -1/2 polarization collision mode in both process e+e- → H0Z0Z0 and e+e- → H0H0Z0 may provide a possibility to improve the sensitivity in probing the LED effects.