Using the first principles method of the full potential linear augmented plane waves (FPLAPW), the structural and the electronic properties of AlBi are investigated. It is found that this compound has a small and direct semiconducting gap at Γ. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the dependences of the volume, the bulk modulus, the variation of the thermal expansion α, as well as the Debye temperature θD and the heat capacity Cv are successfully obtained in the whole range from 0 to 30 GPa and temperature range from 0 to 1200 K.