Structural properties of Alumnum nitride in wurtzite, zinc-blende and rock-salt phases have been investigated by Full Potential-Linearized Augmented Plane Waves method based on Density Functional Theory within Local Density Approximation and seven Generalized Gradient schemes. It is found that, Alumnum nitride in wurtzite phase is the stable ground state structure and makes a transition to rock-salt phase at a low transition pressure (11.54 GPa). According to present total energy calculations, zinc-blende phase of Alumnum nitride also makes a transition to rock-salt phase, at a low transition pressure (10.17 GPa). Generalized Gradient functionals of Perdew-Wang-Engel-Vosko and Perdew-Burke-Ernzerhof are found to be more successful than other approximations considered in this work for providing the closest values of the structural features, such as, lattice constants, bulk moduli, first order pressure derivatives of bulk moduli and cohesive energies of Alumnum nitride three phases to available experimental ones. Although Generalized Gradient approaches of Perdew-Wang-Engel-Vosko, Perdew-Burke-Ernzerhof, Becke-Perdew-Wang and Perdew-Burke-Ernzerhof (revised) are found to be accurate schemes for elastic constants of rock-salt AlN, only Perdew-Wang-Engel-Vosko and Perdew-Burke-Ernzerhof functionals are observed to be more successful than the other schemes for supplying accurately both C-11 and C-12 of zinc-blende Alumnum nitride structure. Perdew-Wang-Engel-Vosko functional is observed to be superior to Perdew-Burke-Ernzerhof for elastic constants of wurtzite Alumnum nitride structure. Elastic constants of wurtzite Alumnum nitride obtained by self Perdew-Wang-Engel-Vosko approach and Martin's transformation calculations in which elastic constants of zinc-blende Alumnum nitride are calculated with Perdew-Wang-Engel-Vosko scheme, are very close to the experimental ones. Hence, functional of Perdew-Wang-Engel-Vosko is decided to be the most accurate approximation among Local Density Approximation and other Generalized Gradient schemes considered in this work for all structural properties of Alumnum nitride three phases.