This paper presents the results of relativistic calculation intended specifically to investigate the dominant states for dielectronic recombination of Li-like into Be-like Al ions in short-pulse laser produced plasmas. The relativistic Dirac R-matrix calculation is performed to output resonance energy levels and rates. The target energies and orbitals are calculated with the extended average level multi-configurational Dirac-Fock method in the general-purpose relativistic atomic structure package. This type of calculation gives a set of 13 bound orbitals that is optimized over all the levels included. The resulting 13 relativistic orbitals produced 74 Jπ levels, all of which are to be used in the close-coupling expansion. To the best of our knowledge, the work reported herein describes for the first time such detailed calculation for this atomic system and the results are relevant to the short-pulse laser produced plasma modeling.