A method for producing a positive active material for a lithium secondary battery containing a lithium transition metal composite oxide having a hexagonal crystal structure in which the transition metal (Me) includes Ni, Co and Mn, wherein when coprecipitating compounds containing Ni, Co and Mn in a solution to prepare a precursor, a solution containing a compound of Ni and Co and a solution containing a Mn compound are simultaneously added dropwise separately, and thereby a precursor of a transition metal composite oxide in which a molar ratio of Ni to the transition metal (Me) is 0.5 or more and 0.9 or less, a molar ratio of Co to the transition metal (Me) is 0.1 or more and 0.3 or less, and a molar ratio of Mn to the transition metal (Me) is 0.03 or more and 0.3 or less, is prepared.