Non-stoichiometric spinel oxides LiMyMn2-yO4-delta (y = 0, 1/6 and 1/3; M = Cr, Co and Ni) (space group Fd (3) over bar m) were prepared by controlling oxygen partial pressure at 1023 K. The single phase region of each LiMyMn2-yO4-delta was larger than that of parent LiMn2O4-delta (0 less than or equal to delta < 0.018). The more the substituted amount y increased in LiMyMn2-yO4, the more the delta extended at 1023 K (e.g. 0 less than or equal to delta < 0.040 for LiCo1/6Mn11/6O4-delta and 0 less than or equal to delta < 0.057 for LiCo1/3Mn5/3O4-delta). The defect model for LiMyMn2-yO4-delta was estimated from the data of the cell volume and the measured density. These defect structures were assumed to form metal excess structure (Li)(8a)[Lidelta/(4-delta)Mdelta y/(4-delta)Mndelta(2-y/(4-delta))](16c)[MyMn2-y](16d)[O-4](32e) which has been the same as that of the parent LiMn2O4-delta published previously. As the cathode for the lithium secondary battery, the initial capacity of LiCo1/6Mn11/6O4-delta with delta = 0.040 had a value of 127 Ah kg(-1). It was about 11% larger than that of the spinel with delta = 0. The spinel with the defect showed a good cycle performance.