A classical trajectory Monte Carlo method is used to investigate the collision ionization of H by He2+ in Debye plasma, and the total and differential cross sections are obtained for collision energies of 5—400 keV/u in a large plasma parameter range. The interaction between charged particles is described by the Debye-Hückel model. Plasma screening changes the ionization energy and classical microcanonical distribution of bound electrons and the interaction between electron and the projectile, which result in the modification of ionization cross sections. It is found that both the total and differential cross sections increase with the increasing of screening interaction, and especially for energies below 10 keV/u, the cross sections are one to two magnitudes larger than those in the unscreened case. The emitted electron moves to the higher energy range, and the binary-encounter ionization mechanism becomes more important and a new hump appears due to the screening effect. Our unscreened cross section is in a good agreement with the experimental measurement for collision energies beyond 70 keV/u.