We calculate the ion-ion correlation effect on the neutrino-nucleus scattering in supernova cores, which is an important opacity source for the neutrinos and plays a vital role in supernova explosions. In order to calculate the ion-ion correlation effect we use the results of the improved hypernetted-chain-method calculations of the classical one-component plasma. As in the preceding studies on this effect, we find a dramatic decrease of the effective neutrino-nucleus scattering cross section for relatively low energy neutrinos with Eν<=20 MeV. As a matter of fact, our calculation shows a much more dramatic reduction of the effective neutrino-nucleus scattering cross section for the low-energy neutrinos with Eν<=10 MeV than the results of Horowitz. Therefore, the ion-ion correlation effect will be more important than has hitherto been recognized. We present an accurate analytic fitting formula that summarizes our numerical results. This fitting formula will facilitate the application of the present results to supernova explosion simulations.