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 . <EOS>