A method for making a composite of cobalt oxide is disclosed. An aluminum nitrate solution is provided. Lithium cobalt oxide particles are introduced into the aluminum nitrate solution. The lithium cobalt oxide particles are mixed with the aluminum nitrate solution to form a mixture. A phosphate solution is added into the mixture to react with the aluminum nitrate solution and form an aluminum phosphate layer on surfaces of the lithium cobalt oxide particles. The lithium cobalt oxide particles with the aluminum phosphate layer formed on the surfaces thereof are heat treated to form a lithium cobalt oxide composite. The lithium cobalt oxide composite is electrochemical lithium-deintercalated at a voltage of Vx, wherein 4.5V