In an active material of a positive electrode for a non-aqueous electrolyte secondary battery where lithium cobaltate represented by the formula LiCoO.sub.2 is used, which comprises a mixture of primary particles of small crystals falling in the range of 0.4 to 10 .mu.m in Feret's diameter in a projection chart by SEM observation and having an average diameter of 5 .mu.m or less and secondary particles formed by gathering of a number of said small crystals and having an average particle size falling in the range of 4 to 30 .mu.m where the molar ratio of Co to Li is 0.97 or more to 1.03 or less, at least part of the small crystals constituting the secondary particles are jointed by sintering and furthermore, the secondary particles are preferably spherical or elliptical. Features also are constituted by an active material of a positive electrode for a non-aqueous electrolyte secondary battery wherein the secondary particles account for 90 percent or more of particles having a Feret's diameter of 9 .mu.m or more and the volume ratio of particles of 6 .mu.m or more is 70 percent or more of the total mixture, which enables improvement of discharge capacity, maintaining index of discharge capacity and high-efficiency discharge capacity and a process for preparing the same and a non-aqueous electrolyte secondary battery where the active material of a positive electrode is used.