The present invention provides a composite oxide that can achieve a high low-temperature output characteristic, a method for manufacturing the same, and a positive electrode active material in which the generation of soluble lithium is suppressed and a problem of gelation is not caused during the paste preparation. A positive electrode active material for non-aqueous electrolyte secondary batteries, including a lithium-metal composite oxide powder including a secondary particle configured by aggregating primary particles containing lithium, nickel, manganese, and cobalt, or a lithium-metal composite oxide powder including both the primary particles and the secondary particle, wherein the secondary particle has a hollow structure inside as a main inside structure, the slurry pH is 11.5 or less, the soluble lithium content rate is 0.5 [96 by mass] or less, the specific surface area is 2.0 to 3.0 [m2/g], and the porosity is 20 to 50 [96].