A positive electrode active material for a non-aqueous secondary battery, comprising: a crystal particle of lithium transition metal oxide containing at least a nickel element and a manganese element as transition metals, and having a layered structure, wherein with respect to a first diffraction peak located at a diffraction angle 2θ of 17° to 20° and a second diffraction peak located at a diffraction angle 2θ of 43° to 46° when an X-ray diffraction measurement is performed on a crystal structure of the crystal particle using a Cu tube, when a first integrated intensity of the first diffraction peak is defined as I A, a second integrated intensity of the second diffraction peak is defined as I B, an integrated intensity ratio between the first integrated intensity and the second integrated intensity is defined as R I, a first height of the first diffraction peak is defined as H A, a second height of the second diffraction peak is defined as H B, and a peak intensity ratio between the first height and the second height is defined as R H, the following relationships are satisfied: R I = I A / I B R H = H A / H B S F = R H / R I, and 1.1 ≤ S F ≤ 2.2 characterized in that when a maximum diameter and a minimum diameter of a primary particle of the lithium transition metal oxide as observed with a scanning electron microscope are defined as L H and Lw, respectively, and a ratio between the maximum diameter and the minimum diameter is defined as R L, the following relationships are satisfied: R L = L H / L W, and 1.3 < R L < 2.1, and the lithium transition metal oxide is represented by a composition formula Li 1+Z (Ni 1-X-Y Mn X M Y) 1-Z O 2, M is at least one element among Co, Al, Fe, Cr and Mg, and the following relationships are satisfied: 0 ≤ Z ≤ 0.2, 0 < X < 0.5, and 0 ≤ Y < 0.4. a crystal particle of lithium transition metal oxide containing at least a nickel element and a manganese element as transition metals, and having a layered structure, wherein with respect to a first diffraction peak located at a diffraction angle 2θ of 17° to 20° and a second diffraction peak located at a diffraction angle 2θ of 43° to 46° when an X-ray diffraction measurement is performed on a crystal structure of the crystal particle using a Cu tube, when a first integrated intensity of the first diffraction peak is defined as I A, a second integrated intensity of the second diffraction peak is defined as I B, an integrated intensity ratio between the first integrated intensity and the second integrated intensity is defined as R I, a first height of the first diffraction peak is defined as H A, a second height of the second diffraction peak is defined as H B, and a peak intensity ratio between the first height and the second height is defined as R H, the following relationships are satisfied: R I = I A / I B R H = H A / H B S F = R H / R I, and 1.1 ≤ S F ≤ 2.2 characterized in that when a maximum diameter and a minimum diameter of a primary particle of the lithium transition metal oxide as observed with a scanning electron microscope are defined as L H and Lw, respectively, and a ratio between the maximum diameter and the minimum diameter is defined as R L, the following relationships are satisfied: R L = L H / L W, and 1.3 < R L < 2.1, and the lithium transition metal oxide is represented by a composition formula Li 1+Z (Ni 1-X-Y Mn X M Y) 1-Z O 2, M is at least one element among Co, Al, Fe, Cr and Mg, and the following relationships are satisfied: 0 ≤ Z ≤ 0.2, 0 < X < 0.5, and 0 ≤ Y < 0.4.