Manufacturing method of positive active material precursor positive active material for lithium secondary battery, cathode and lithium secondary battery comprising the positive active material

Provided is a method of manufacturing a positive active material precursor for a lithium secondary battery including the steps of: preparing a mixed solution of a metal compound containing a nickel compound, a manganese compound, and a cobalt compound; adding an acid-based complex-forming agent to the mixed solution of the metal compound to form a complex through a chelation reaction between a positive ion of the metal compound and a negative ion of the complex-forming agent; and substituting a hydroxide ion for the negative ion of the complex to perform a coprecipitation. Also, provided are a method of manufacturing a positive active material for a lithium secondary battery, a cathode including the positive active material, and a lithium secondary battery including the cathode. In accordance with, the positive active material precursor for th lithium secondary battery, the positive active material, the cathode, and the lithium secondary battery may be environment-friendly manufactured.