In this manuscript, we investigate the effect of structural disorder on the physical properties of Pd-based Heusler alloys: PdCoMnAl, Pd2CoAl and Pd2MnAl using first-principles calculations. In fact, we are studying the structural properties of the equatorial quaternary Heusler alloy PdCoMnAl for three phases: type 1, type 2 and type 3, we have carried out this property to determine the most stable phases. The structural properties results show that the phase of type I, of this alloy is the most stable configuration. In addition, the band structures, and density of states calculations results show that this compound exhibits a half-metallic character with a 100% of spin polarization (SP) at the Fermi-level. The total magnetic moment of the Heusler compound is found to be 5.00 µB. Moreover, it is found that the Slater-Pauling is well described for this alloy. On the other hand, concerning total energy of the full Heusler Pd2YAl (Y = Co or Mn) alloys. It is found that such material in L21-type structure is always smaller than in the XA-type structure during the whole lattice variation variety and the L21-type structure is more energetically preferable for the both full alloys. In addition, the density of states at the Fermi level within the spin up and down states show the metallicity of these compounds. Our results show that the quaternary Heusler is a potential candidate for the spintronic applications.