We have developed an efficient grid method that can accurately deal with the electronic wave packet dynamics of two-electron systems in three-dimensional (3D) space. By using the dual transformation technique, we remove the numerical difficulties arising from the singularity of the attractive Coulomb potential. Electron-electron repulsion is incorporated into the wave packet propagation scheme without introducing any approximations. The exact electronic dynamics of H-2 is simulated for the first time. At small internuclear distances (e.g., R=4 a.u.), an ionic component characterized by the structure H+H- is created in an intense laser field epsilon (t) (intensity > 10(13) W/cm(2) and lambda approximate to 720 nm) because an electron is transferred from the nucleus around which the dipole interaction energy for the electron becomes higher with increasing \epsilon (t)\. The localized ionic structure is identified with the H- anion at the nucleus around which the dipole interaction energy becomes lower. Tunneling ionization proceeds via the formation of such a localized ionic structure, and direct ionization from the covalent structure is much smaller; the localized ionic structure plays the dominant doorway state to ionization of H-2.