We report a systematic first-principles study of structural properties, electronic structures and magnetic properties of Cr doped ZnTe with the Cr concentration up to 0.5. We fully optimize all the structures concerned, both ferromagnetic and antiferromagnetic, and their internal atomic positions. Our calculations show that they are half-metallic ferromagnets with half-metallic gaps over 0.6 eV. Our calculated results are consistent with the fact that only those bulk samples with very small doping concentrations can be stable thanks to the entropy effect. On the other hand, up to 20% Cr doping concentrations have been achieved experimentally in thin films fabricated with nonequilibrium methods. Our calculated results indicate that half-metallic ferromagnetism can be realized in high-quality thin film samples of Cr_xZn_1−xTe with nonequilibrium methods. We explain the half-metallic ferromagnetism in terms of a pd hybridization and resulting large exchange splitting of d-dominated bands. Compatible with appropriate semiconductors, these materials, at least some of them, could be useful in spintronics.