A spin-polarized version of the tight-binding Green's function scheme is developed for GaAs:Cr2+(3d4) system, which is under hydrostatic pressure and is alloyed with AlAs in different concentration. Results on the variation trends of 5E excited and 5T2 ground acceptor levels of GaAs:Cr2+ with different pressures and aluminum concentrations are reported. The theory shows that under certain pressure and Al concentration the 5E state will shift into the band gap from the bottom of conduction band. The 5E→5T2 luminescence which can not be observed in normal condition will appear in such case. Good overall agreement between theory and experiment is found. The theory also predicts that the similar luminescence process-would occur when GaAs is alloyed with Gap in certain concentration, but this still waits for experimental verification.