Rechargeable lithium ion battery

A rechargeable lithium ion battery with high power density comprises a positive electrode; a negative electrode; and a non-aqueous electrolytic solution, in which the positive electrode includes a active material layer containing a positive electrode active material with the particle diameter of 5 µm or less and having the thickness at a range of 20 to 80 µm. Another rechargeable lithium ion battery with high power density comprises a positive electrode; a negative electrode; and a non-aqueous electrolytic solution, in which the positive electrode has two active material layers, each of which contains a positive electrode active material with a different diameter and has the thickness at a range of 20 to 30 µm.