Positive active material for lithium secondary battery, precursor of positive active material, electrode for lithium secondary battery and lithium secondary battery

Provided is a positive active material for a lithium secondary battery or a lithium secondary battery using the positive active material, in which the positive active material includes a lithium transition metal composite oxide having an ±-NaFeO 2 -type crystal structure and represented by the composition formula of Li 1+± Me 1-± O 2 (Me is a transition metal including Co, Ni and Mn and ± > 0). The positive active material contains Na in an amount of 900 ppm or more and 16000 ppm or less, or K in an amount of 1200 ppm or more and 18000 ppm or less. Also provided is a method for production of the positive active material for a lithium secondary battery. In a sintering step, to a carbonate precursor containing Na or K and represented by MeCO 3 (Me is a transition metal including Co, Ni and Mn) are added a sodium compound or a potassium compound together with a lithium compound.