Out-of-plane thin magnetic tunnel junctions with giant magnetic anisotropy constant (K-i) are of great interest for magnetic memory devices because a large K-i provides both high thermal stability and low switching currents. Here, we proposed that heavy elements capping has dramatic consequences on the K-i magnitude and can be substantially enhanced with a suitable capping material. Using ab-initio density functional theory calculations, we systematically investigate the influence of 184d/5d transition and 5p/6p post-transition metals capping layers on the K-i in MgO/Co thin film structure. A relatively large K-i is found for 6 capping materials including Tc, Re, Ir, Pt, Au, and Bi. Particularly, MgO/Co/Pt and MgO/Co/Au structures established an exceptionally giant K-i of 4.12 and 4.54 mJ/m(2), respectively. The results are explained in terms of the layer and atom-resolved contributions from different orbitals hybridization. The present findings provoke towards achieving high thermal stability in low dimension magnetic tunnel junctions to build high-density magnetic memory devices.