We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen,Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB2 compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Dcbye model, obtained successfully are the dependences of the normalized lattice parameters a/a0 and c/c0 on pressure P, the normalized primitive cell volume V/Vo on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature θD and the heat capacity CV on pressure P and temperature T.