This paper concerns the modification of thermal properties of aluminum nitride polycrystalline ceramic material with high thermal conductivity coefficient. The way to change these properties was to distribute graphene particles in the high-conductive matrix. The composite material was hot-pressed at 1900 °C under 25 MPa pressure. The applied pressure allowed to orient the graphene particles and obtain an anisotropy of thermal conductivity. The microstructural observations were made by SEM method. The phases of the matrix were analyzed by XRD measurements, and the existence of graphene was confirmed by Raman spectroscopy. The quantity of graphene in the material after hot-pressing process was determined by thermogravimetric examinations in air flow. The thermal phase stability was checked by differential scanning calorimetry with mass change record. The thermal expansion coefficient was measured by dilatometric method. The thermal diffusivity and thermal conductivity were measured in various directions of the material. The results showed that the anisotropy of thermal conductivity exceeds 100 % for material with 10 mass% of graphene (GPLs). The introduced 2D particles caused a decrease of this parameter in the parallel direction to the load applied during the hot-pressing process.