The thermal consants and the thermal properties of the Cu doped wurrite type ZnO was investigated based on the linear response density perturbation functional theory. The results showed that Cu doping could cause the decrease of ZnO oxide unit cell,and the lattice heat capacity increased with increasing temperature for both pure ZnO and Cu doped ZnO systems, and the Cu doped system had larger lattice heat capacity. The maximum temperature reached to 69.1 J·mol-1·K-1 and 152.8 J·mol-1·K-1 respectively for pure ZnO and the Cu doped ZnO at 900 K.The Debye temperature increased with increasing temperature for both systems, and the Cu doped system had higher Debye temperature value than that of the pure ZnO system below 175 K;the Debye temperature value went lower than that of the pure ZnO system above 175 K.New vibrational modes were introduced by Cu doping,and the Cu doped ZnO system had higher lattice thermal conductivity.