To provide a lithium manganese composite oxide capable of improving the initial discharge capacity of secondary batteries by removing more Li ions than the conventional lithium manganese composite oxide does when used in the positive electrode used for secondary batteries. A lithium manganese composite oxide having a Li2MnO3 type crystal structure, wherein a part of Li and/or Mn in a lithium manganese oxide represented by a formula Li2MnO3 is substituted by one or more doping elements M selected from the group consisting of Ti, Zr, Hf, V, Nb, Ta, Si, Ge, Sn, P, Sb and Bi. The above-described lithium manganese composite oxide, wherein the doping elements are P and/or Si. A positive electrode used for nonaqueous electrolyte secondary batteries, comprising the above-described lithium manganese composite oxide. A nonaqueous electrolyte secondary battery comprising the above-described positive electrode used for nonaqueous electrolyte secondary batteries.