A lithium-titanium composite oxide includes a crystallite diameter not larger than 6.9.times.10.sup.2 .ANG., and includes a rutile type TiO.sub.2, an anatase type TiO.sub.2, Li.sub.2TiO.sub.3 and a lithium titanate having a spinel structure. The rutile type TiO.sub.2, the anatase type TiO.sub.2 and Li.sub.2TiO.sub.3 each has a main peak intensity not larger than 7 on the basis that a main peak intensity of the lithium titanate as determined by the X-ray diffractometry is set at 100.