A method for producing a positive electrode active material for nonaqueous electrolyte secondary batteries, the positive electrode active material being represented by a general formula: Li a Ni 1-x-y Co x M y W z O 2+α (where 0 ≤ x ≤ 0.35, 0 ≤ y ≤ 0.35, 0.0005 ≤ z ≤ 0.030, 0.97 ≤ a ≤ 1.25, 0 ≤ α ≤ 0.20, and M is at least one element selected from Mn, V, Mg, Mo, Nb, Ti and Al), the method comprising: a mixing step and water washing step of using, as a base material, a lithium-metal composite oxide powder represented by a general formula: Li c Ni 1-x-y Co x M y O 2 (where 0 ≤ x ≤ 0.35, 0 ≤ y ≤ 0.35, and 0.97 ≤ c ≤ 1.25 are satisfied, and M is at least one element selected from Mn, V, Mg, Mo, Nb, Ti and Al) and composed of primary particles and secondary particles formed by aggregation of the primary particles, adding a tungsten compound powder having a solubility A of 2.0 g/L or less that is determined by stirring for 20 minutes in water having a pH of 12.5 at 25°C, to the lithium-metal composite oxide powder, either by mixing the lithium-metal composite oxide powder with water to form a slurry and the tungsten compound is added in powder form into the slurry or by giving the tungsten compound powder into water in advance and then the lithium-metal composite oxide powder is added into the water, and stirring to mix them, followed by solid-liquid separation to disperse the tungsten compound powder in the lithium-metal composite oxide powder to thereby obtain a tungsten-containing mixture containing excess lithium of the lithium-metal composite oxide powder dissolved in the water washing of the lithium-metal composite oxide powder, excess lithium of the lithium-metal composite oxide powder not dissolved, and lithium in crystal of the lithium-metal composite oxide; and a heat-treating step of heat-treating the tungsten-containing mixture obtained in the mixing step to uniformly disperse tungsten on a surface of the primary particles of the lithium-metal composite oxide powder, and thereafter form a compound containing tungsten and lithium from the tungsten dispersed uniformly on the surface of the primary particles and lithium in the tungsten-containing mixture, on the surface of the primary particles of the lithium-metal composite oxide powder. a mixing step and water washing step of using, as a base material, a lithium-metal composite oxide powder represented by a general formula: Li c Ni 1-x-y Co x M y O 2 (where 0 ≤ x ≤ 0.35, 0 ≤ y ≤ 0.35, and 0.97 ≤ c ≤ 1.25 are satisfied, and M is at least one element selected from Mn, V, Mg, Mo, Nb, Ti and Al) and composed of primary particles and secondary particles formed by aggregation of the primary particles, adding a tungsten compound powder having a solubility A of 2.0 g/L or less that is determined by stirring for 20 minutes in water having a pH of 12.5 at 25°C, to the lithium-metal composite oxide powder, either by mixing the lithium-metal composite oxide powder with water to form a slurry and the tungsten compound is added in powder form into the slurry or by giving the tungsten compound powder into water in advance and then the lithium-metal composite oxide powder is added into the water, and stirring to mix them, followed by solid-liquid separation to disperse the tungsten compound powder in the lithium-metal composite oxide powder to thereby obtain a tungsten-containing mixture containing excess lithium of the lithium-metal composite oxide powder dissolved in the water washing of the lithium-metal composite oxide powder, excess lithium of the lithium-metal composite oxide powder not dissolved, and lithium in crystal of the lithium-metal composite oxide; and a heat-treating step of heat-treating the tungsten-containing mixture obtained in the mixing step to uniformly disperse tungsten on a surface of the primary particles of the lithium-metal composite oxide powder, and thereafter form a compound containing tungsten and lithium from the tungsten dispersed uniformly on the surface of the primary particles and lithium in the tungsten-containing mixture, on the surface of the primary particles of the lithium-metal composite oxide powder.