The effect of annealing conditions on the magnetic characteristics of multilayered perpendicular magnetic tunnel junctions (pMTJs) of the structures SiNx/Pt/TbFeCo/MgO/(Co/Pt)5 and SiNx/Pt/TbFeCo/Mg/MgO/(Co/Pt)5 with various MgO barrier thicknesses are explored. We found that both the hard and free layers have coercivity reduction with increasing annealing temperature. However, annealing at median temperature could improve the squareness of the hysteresis loop of the hard layer (TbFeCo). More interestingly, the annealing temperature at which the free layer (Co/Pt) lost the perpendicular magnetic anisotropy (PMA) depends on the thickness of the MgO layer. Insertion of a thin Mg layer of thickness 0.4 nm between the barrier and the hard layer can assist the junction in keeping the PMA at higher annealing temperature. The experimental results suggest that 150 °C could be the suitable annealing temperature for these pMTJs.