Heyd-Scuseria-Ernzerh of screened hybrid density functional was used to calculate the band gap and the formation enthalpy of Cd1-xZnxTe alloys, which are much more accurate than the traditional GGA methods. Special quasirandom structure was used to describe the disordered Cd1-xZnxTe alloys. The band gap bowing parameter of Cd1-xZnxTe alloys is 0.266eV, which is consistent with the experimental value of about 0.254eV. The calculated results show that the formation enthalpy of Cd1-xZnxTe alloys is relatively high, especially for Cd0.5Zn0.5Te alloy (25.60meV/atom). The difference between local bond lengths of Cd-Te and Zn-Te that are very close to those in bulk CdTe and ZnTe is quite large, indicating that the large relaxation exists in these alloys and this relaxation may lead to the large formation enthalpy described above.