NOVELTY - A lithium complex oxide sintered compact is obtained by sintering microparticles of lithium complex oxide. The sintered compact has peak pore diameter providing maximum differential pore volume value of 0.80-5 mu m in pore diameter of 0.01-10 mu m, and total pore volume of 0.10-2 mL/g, measured using mercury porosimeter, average particle diameter of 20 mu m or less which is more than the value of peak pore diameter, measured by laser diffraction/scattering-type particle size distribution method, and Brunauer-Emmett-Teller specific surface area of 1-10 m2/g.    USE - Lithium complex oxide sintered compact is used for battery positive electrode composition for lithium ion battery (both claimed) used as power supply. Uses include but are not limited to mobile telephone, notebook computer, digital camera, electrical vehicle and motor vehicle.    ADVANTAGE - The lithium complex oxide sintered compact provides lithium ion battery having high-speed discharge characteristics.    DETAILED DESCRIPTION - A lithium complex oxide sintered compact is obtained by sintering microparticles of lithium complex oxide. The lithium complex oxide sintered compact has peak pore diameter providing maximum differential pore volume value of 0.80-5 mu m in pore diameter of 0.01-10 mu m, and total pore volume of 0.10-2 mL/g, measured using mercury porosimeter, average particle diameter of 20 mu m or less which is more than the value of peak pore diameter, measured by laser diffraction/scattering-type particle size distribution method, subpeak providing differential pore volume of 10% or more of maximum differential pore volume on the smaller pore diameter side with respects to the peak pore diameter that the pore size corresponding to the subpeak is 0.50-2 mu m, Brunauer-Emmett-Teller specific surface area of 1-10 m2/g and half value width of strongest peak of 0.10-0.030 deg with respect X-ray diffraction peaks, in X-ray diffraction measurement. An INDEPENDENT CLAIM is included for battery positive electrode composition.