The thermal constants and thermal transport properties of the Ga doped wurtzite type ZnO were investigated by ab-initial calculations based on the density functional theory as well as the linear response density perturbation functional theory. The results show that the Ga doped wurtzite type ZnO has increased lattice. The lattice heat capacity increases with increasing temperature for both systems, and the heat capacities reach 16.5 Cal.mol-1K-1 and 31.3 Cal.mol-1K-1 for the pure ZnO and the Ga doped ZnO at 900 K, respectively. The Debye temperature increases with increasing temperature for both systems. There are new vibrational modes that is introduced by Ga doping.