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.