In a lithium secondary battery provided with a positive electrode, a negative electrode, and a non-aqueous electrolyte, a tungsten oxide W.sub.20 O.sub.58 or W.sub.18 O.sub.49, or the tungsten oxide to which lithium is added, or a tungsten composite oxide comprising a tungsten oxide containing at least one type of metal element selected from the group consisting of Mn, Cu, V, Cr, Fe, Co, and Ni and having a W.sub.20 O.sub.58 -type or W.sub.18 O.sub.49 -type crystal structure or the tungsten composite oxide to which lithium is added is used as a positive electrode active material for said positive electrode or a negative electrode active material for said negative electrode.