The lattice parameter, bulk modulus and its pressure derivative of the wurtzite-type aluminium nitride (w-AlN)are investigated by using the Cambridge Serial Total Energy Package (CASTEP) program in the framework of Density Functional Theory (DFT). The calculated results are in good agreement with the available experimental data and other theoretical results. Through the quasi-harmonic Debye model, the dependences of the normalized lattice parameters a/a0 and c/c0, axial ratio c/a, normalized primitive-cell volume V/V0, Debye temperature ΘD and heat capacity Cv on pressure P and temperature T are obtained. It is found that the interlayer covalent interactions (Al-N bonds) are more (even a little) sensitive to temperature and pressure than intralayer ones (N-N bonds), which gives rise to a little lattice anisotropy in the w-AlN.