The random occupancy of hydrogen atoms or proton disorder is the most unique feature of ice crystal. Taking the cubic Ic ice as an example, we study the impact of proton disorder on various physical properties by first-principles calculation in density-functional theory for the first time. Our results show that the dielectric polarization enhances the cohesion of H2O molecules, thus increases the bulk modulus of Ic ice. The shear elastic constants are more sensitive to dielectric polarization than the elastic constant of normal strain. Ic ice is a semiconductor with a wide direct bandgap of 5.54 eV. The disorder of electric dipole moments raises the valence bands and decreases the energy bandgap. The average dielectric constant is less affected by the disorder. The present conclusions also keep valid for the more common hexagonal Ih ice based on its similar local structure with Ic ice. © 2012 Wiley Periodicals, Inc.