Provided is a lithium metal compound oxide having a layered structure, which is very excellent as a positive electrode active material of a battery that is mounted on, particularly, an electric vehicle or a hybrid vehicle.Suggested is a lithium metal compound oxide having a layered structure which is expressed by general formula of Li1+xM1−xO2 (M represents metal elements including three elements of Mn, Co, and Ni). In the lithium metal compound oxide having a layered structure, D50 is more than 4 μm and less than 20 μm, a ratio of a primary particle area to a secondary particle area of secondary particles having a size corresponding to the D50 (“primary particle area/secondary particle area”) is 0.004 to 0.035, and the minimum value of powder crushing strength that is obtained by crushing a powder using a microcompression tester is more than 70 MPa.