Ab initio calculations based on the density functional theory (DFT) have been employed to explore the half-metallicity and magnetic properties of the CrZrZ (Z = In, Sn, Sb, and Te) half-Heusler compounds. All the CrZrZ (Z = In, Sn, Sb, and Te) half-Heusler compounds are predicted to have a half-metallic character. The CrZrZ (Z = In, Sn, Sb, and Te) half-Heusler compounds have total magnetic moments of 5.0, 4.0, 3.0, and 2.0 A mu (B)/formula unit (f.u.), respectively, which agrees with the Slater-Pauling rule m (tot) = z (tot) - 18. The value of the magnetic moment of CrZrIn compound is expected to reach as high as 5 A mu (B)/f.u. All the CrZrZ materials have an energy gap in the spin-up channel of 1.02, 1.23, 1.35, and 0.71 eV for Z = In, Sn, Sb, and Te, respectively, and keep half-metallicity within the wide range of lattice constants. The Curie temperatures of the CrZrZ (Z = In, Sn, Sb, and Te) compounds are estimated to be 1770, 1481, 835, and 1020 K, respectively, using the mean field approximation (MFA).