A positive electrode active material obtainable by a method of preparing the positive electrode active material, the positive electrode active material comprising a positive electrode active material particle containing a composite oxide having a hexagonal crystal structure, wherein the composite oxide has an average composition represented by the following formula: Li x Co y M1 1-y O 2... and includes Li, Co, and at least one element M1 selected from the group consisting of Mg, Al, and Ti, wherein x and y satisfy 0.95 ≤ x ≤ 1.0 and 0 < y < 1, the at least one element M1 is present on a surface of the positive electrode active material particle, an atomic ratio (total amount of the at least one element M1/Co amount) of an amount of Co on the surface of the positive electrode active material particle and a total amount of the at least one element M1 is 0.6 or more and 1.3 or less, a half-value width of a peak of an A 1g vibration mode of the hexagonal crystal structure in a Raman spectrum is 10 cm -1 or more and 17 cm -1 or less, wherein the half-value width is a full width at half maximum, and a peak intensity ratio IA 1g-H /IE g of a peak intensity IA 1g-H of the A 1g vibration mode of the hexagonal crystal structure in the Raman spectrum and a peak intensity IE g of an E g vibration mode of the hexagonal crystal structure is 1.1 or more and 1.9 or less, wherein the Raman spectrum is measurable as indicated in the description, the method of preparing the positive electrode active material comprising: preparing a powder of composite oxide particles containing Li, Co, and the at least one element M1 and having the hexagonal crystal structure, obtaining a mixture by mixing the prepared composite oxide particle powder, a lithium salt, cobalt oxide, and at least one compound selected from the group consisting of a Mg-containing compound, an Al-containing compound, and a Ti-containing compound and adjusting, at this time, a compounding ratio of each material so that the atomic ratio of the amount of Co on the surface of the positive electrode active material particles and the total amount of at least one element M1 is 0.6 or more and 1.3 or less, wherein the lithium salt is lithium carbonate or at least one of lithium phosphate, lithium fluoride and lithium sulfide, stirring the mixture at high speed, and heat-treating and finely pulverizing the mixture to obtain the positive electrode active material. wherein the composite oxide has an average composition represented by the following formula: Li x Co y M1 1-y O 2... and includes Li, Co, and at least one element M1 selected from the group consisting of Mg, Al, and Ti, wherein x and y satisfy 0.95 ≤ x ≤ 1.0 and 0 < y < 1, the at least one element M1 is present on a surface of the positive electrode active material particle, an atomic ratio (total amount of the at least one element M1/Co amount) of an amount of Co on the surface of the positive electrode active material particle and a total amount of the at least one element M1 is 0.6 or more and 1.3 or less, a half-value width of a peak of an A 1g vibration mode of the hexagonal crystal structure in a Raman spectrum is 10 cm -1 or more and 17 cm -1 or less, wherein the half-value width is a full width at half maximum, and a peak intensity ratio IA 1g-H /IE g of a peak intensity IA 1g-H of the A 1g vibration mode of the hexagonal crystal structure in the Raman spectrum and a peak intensity IE g of an E g vibration mode of the hexagonal crystal structure is 1.1 or more and 1.9 or less, wherein the Raman spectrum is measurable as indicated in the description, the method of preparing the positive electrode active material comprising: preparing a powder of composite oxide particles containing Li, Co, and the at least one element M1 and having the hexagonal crystal structure, obtaining a mixture by mixing the prepared composite oxide particle powder, a lithium salt, cobalt oxide, and at least one compound selected from the group consisting of a Mg-containing compound, an Al-containing compound, and a Ti-containing compound and adjusting, at this time, a compounding ratio of each material so that the atomic ratio of the amount of Co on the surface of the positive electrode active material particles and the total amount of at least one element M1 is 0.6 or more and 1.3 or less, wherein the lithium salt is lithium carbonate or at least one of lithium phosphate, lithium fluoride and lithium sulfide, stirring the mixture at high speed, and heat-treating and finely pulverizing the mixture to obtain the positive electrode active material. preparing a powder of composite oxide particles containing Li, Co, and the at least one element M1 and having the hexagonal crystal structure, obtaining a mixture by mixing the prepared composite oxide particle powder, a lithium salt, cobalt oxide, and at least one compound selected from the group consisting of a Mg-containing compound, an Al-containing compound, and a Ti-containing compound and adjusting, at this time, a compounding ratio of each material so that the atomic ratio of the amount of Co on the surface of the positive electrode active material particles and the total amount of at least one element M1 is 0.6 or more and 1.3 or less, wherein the lithium salt is lithium carbonate or at least one of lithium phosphate, lithium fluoride and lithium sulfide, stirring the mixture at high speed, and