We have investigated the phase transition, the structural and the thermodynamic properties of AlAs in three crystallographic structures, i.e. B3 （zinc blende）, B1 （rocksalt）, and B8 （nickel arsenide）, at high pressures by using the full-potential linearized muffin-tin orbital scheme in the framework of density functional theory. By taking the common tangent to the energy-volume curves of B3-B8 and B3-B1 structures, we obtain a pressure of about 5.44 GPa for the transition from B3 to B8 and forecast a transition pressure of about 6.46 GPa for the transition from B3 to B1. We have also investigated the structural properties of B8 under high pressures, the results show that c/a ratio keeps nearly constant （～0.2% fluctuation） when V/V0≈0.7—1.05; c/a ratio increases linearly with the value of V/V0 decreasing when V/V0≈0.4—0.7. The relation between relative volume V/V0 and pressure P is obtained by fitting equation of state （EOS）, and the EOS of B8 accords well with measurements. Finally according to quasi-harmonic Debye model the dependences of bulk module B on pressure P and heat capacity CV on temperature T under different pressures are successfully obtained.