Magnetic properties of Co film in Pt/Co/α-Cr2O3/Pt/α-Al2O3 structure were investigated. Co layer thickness tCo dependence of perpendicular magnetic anisotropy energy density K reveals that the bulk magnetic anisotropy plays an important role in the system in addition to the interfacial anisotropy. Damping constant α monotonically increases with the decrease of tCo but not proportionally to 1/tCo. Both K and α increase with the increase of Pt layer thickness tPt from 3 nm to 5 nm and keeps almost constant in the tPt range between 5 nm to 20 nm. These results are of importance to understand the magnetization switching behavior driven by the magneto-electric (ME) effect as well as to design the spintronics device using the ME effect.