Based on density functional perturbation theory (DFPT) combined with the norm-conserving pseudopotential method，the lattice dynamic simulation is presented. The total phonon density of states，partial phonon density of states and phonon dispersion spectrum of YAG are obtained. By using the special point sampling method within the first Brillouin zone，the special heat capacity and the population averaged group speed of phonon of YAG are calculated. The anharmonic phonon mean free path is calculated theoretically within anharmonic interaction and by using the Fermis golden rule scheme combined with the special point sampling method within the first Brillouin zone. We comprehensively considered two types of the phonon scattering mechanisms，the thermal conductivity of YAG ceramic is obtained. The result indicates that the grain boundary scattering plays a major role in the thermal resistance at low temperature in YAG ceramic，while the three-phonon interaction contribution to the thermal resistance will prevail above a certain temperature. Meanwhile，the viewpoint held by Y. Sato et al. that the difference of the thermal conductivity of between YAG ceramic and single crystal can be ignored above room temperature is theoretically proved. The temperature variations of the calculated thermal conductivity and special heat capacity agree well with the experimental results.